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Exercise 3.3 (NCERT) – Pair of Linear Equations in Two Variables, Class 10

Chapter 3 Exercise 3.3 Class 10

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Below are the solutions of every question of exercise 3.3 of chapter 3, Pair of Linear Equations in Two Variables, NCERT of class 10. YouTube video tutorial of every question is also embedded along with the written solution.  

Question 1

Solve the following pair of linear equations by the elimination method and the substitution method.

(i) x + y = 5 and 2x – 3y = 4

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Elimination Method

Substitution Method

Answer: x = 19/5, y = 6/5

(ii) 3x + 4y = 10 and 2x – 2y = 2

Elimination Method

Substitution Method

Answer: x = 2, y = 1

(iii) 3x – 5y – 4 = 0 and 9x = 2y + 7

Elimination Method

Substitution Method

Answer: x = 9/13, y = -5/13

(iv) x/2 + 2y/3 = -1

       x – y/3 = 3

Elimination Method

Substitution Method

Answer: x = 2, y = 3

Question 2

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

(i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction?

Condition 1

Condition 2

Subtract (i) from (ii) to eliminate y

Substitute in (i)

Answer: 3/5

(ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Let Nuri’s age = x

& Sonu’s age = y

Condition 1: 5 Years ago

Condition 2: 10 Years later

Subtract (ii) from (i) to eliminate x

Substitute in (ii)

Answer: Nuri’s Age = x = 50 Years, Sonu’s Age = y = 20 Years

(iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Let tens digit x

units digit y

Number = 10x + y

Reversed Number = 10y + x

Condition 1

Sum of digits = 0

=> x + y = 9    … (i) 

Condition 2

9 times number = 2 times number obtained by reversing the digits

Add (1) and (2) to eliminate y

Substitute x in 1

The number is : 18

Answer: 18

(iv) Meena went to a bank to withdraw Rs. 2000. She asked the cashier to give her Rs. 50 and Rs. 100 notes only. Meena got 25 notes in all. Find how many notes of Rs. 50 and Rs. 100 she received.

Let ₹50 notes = x

& Let ₹100 notes = y

Condition 1

Total notes = 25

Condition 1

Total money = 2000

Subtract (1) and (2) to eliminate x

Substitute y in 1

Answer: Rs. 50 Notes = 10, Rs. 100 Notes = 15

(v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs. 27 for a book kept for seven days, while Susy paid Rs. 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Let fixed charge = x

Extra charge/day = y

Condition 1

Saritha paid Rs. 27 for 7 days

Condition 2

Susy paid Rs. 21 for 5 days

Subtract (2) and (1) to eliminate x

Substitute y in (ii)

Answer: Fixed Charges = x = Rs. 15, Additional Per Day Charge = Rs. 3

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]]> Exercise 3.2 (NCERT) – Pair of Linear Equations in Two Variables, Class 10 – All Solutions https://mathemafia.com/exercise-3-2-ncert-pair-of-linear-equations-in-two-variables-class-10-all-solutions/ Sun, 04 May 2025 13:15:27 +0000 https://mathemafia.com/?p=18040 Exercise 3.2, chapter 3, Pair of Linear Equations in Two Variables, Class 10 - All questions are solved using Mathematical symbols and scalable vector graphics. The exercise is primarily about Substitution method.

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Exercise 3.2 (NCERT) – Pair of Linear Equations in Two Varibales, Class 10

Chapter 3 Exercise 3.2 Class 10

Below are the Quick links for all questions of Exercise 3.2, Pair of Linear Equations in Two Variables, Class 10. Click a link to view the solution of corresponding question.

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Below are the solutions of every question of exercise 3.2 of chapter 3, Pair of Linear Equations in Two Variables, NCERT of class 10. YouTube video tutorial of every question is also embedded along with the written solution.  

Question 1

Solve the following pair of linear equations by the substitution method.

(i) x + y = 14

     x – y = 4

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Answer: x = 9, y = 5

(ii) s – t = 3

      s/3 + t/2 = 6

Answer: s = 9, t = 6

(iii) 3x – y = 3

       9x – 3y = 9

Conclusion:

Since 9 = 9 is a true identity, hence the lines are coincident. 

In other words, both equations represent the same line.

The system is consistent and has infinitely many solutions

(iv) 0.2x + 0.3y = 1.3

       0.4x + 0.5y = 2.3

From equation (1)

Answer: x = 2, y = 3

(v) √2x + √3y = 0

      √3x – √8y = 0

From equation (1)

Substitute the value of x in equation (2)

Substitute the value of y in expression:

Answer: x = 0, y = 0

(vi) 3x/2 – 5y/3 = -2

      x/3 + y/2 = 13/6

Let’s simplify equation (1)

Let’s simplify equation (2) as well

From equation (4)

Substitute the value of x in equation (3)

Substitute the value of y in expression

Answer: x = 2, y = 3

Question 2

Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

From equation (1)

Substitute the value of x in equation (2)

Substitute the value of y in expression

Answer: x = -2, y = 5

Let us solve the Part 2

Answer: m = -1

Question 3

Form the pair of linear equations for the following problems and find their solution by substitution method.

(i) The difference between two numbers is 26 and one number is three times the other. Find them.

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Let the two numbers be x and y

Condition 1:

Difference between the two numbers = 26

=> x – y = 26 … (1) 

Condition 2:

One number is three times the other

=> x = 3y … (2) 

Let’s apply substitution method

Substitute the value of x from (2) into (1)

Substitute the value of y into eq (2)

x = 3 (13) = 39

Answer: x = 39, y = 13

(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Let the two angles be x (larger) and y (smaller)

Condition 1:

Angles are supplementary

=> x + y = 180° … (1)

Condition 2:

Difference is 18°

=> x – y = 18° … (2)

Let’s apply substitution method

x = y + 18° … (from 2)

Substitute this value of x into (1)

Substitute y = 81 into (2)
x = y + 18 
x = 81 + 18 = 99 

Answer: 99°, 81°

(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs. 3800. Later, she buys 3 bats and 5 balls for Rs. 1750. Find the cost of each bat and each ball.

Let the cost of one bat be x and one ball be y

Condition 1:

Cost of 7 bats and 6 balls = 3800

=> 7x + 6y = 3800 … (1)

Condition 1:

Cost of 3 bats and 5 balls = 1750

=> 3x + 5y = 1750 … (2)

Let’s apply substitution method

From equation (2)

Substitute the value of x into equation (1)

Substitute the value of y into the expression for x

Answer: Cost of 1 bat = Rs. 500, Cost of 1 Ball = Rs. 50

(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

Let the fixed charge be x

& the charge per km be y

Conditions:

For 10 km, total charge = Rs. 105

For 15 km, total charge = Rs. 155

From equation (1) 

Substitute the value of x into equation (2)

Substitute the value of y into equation (3)

Answer: Fixed Charges = Rs. 5, Charges per KM = Rs. 10

Part 2 – Total Fare to travel 25 KM

Answer: Total Fare = Rs. 255

(v) A fraction becomes 9/11 , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.

Condition 1:

Adding 2 to numerator and denominator

Condition 2:

Adding 3 to numerator and denominator

From equation (2)

Substitute the value of x into equation (1)

Substitute the value of y into equation (3)

(vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

Let present age of Jacob = x

& present age of Jacob’s son = y

After 5 Years 5 Years Ago
Jacob’s Age
x + 5
x – 5
Age of Jacob’s son
y + 5
y – 5
Condition
x + 5 = 3 (y + 5) … (1)
x – 5 = 7 (y – 5) … (2)

Let us simplify equation (1) and (2)

From equation (3)

Substitute the value of x into equation (4)

Substitute the value of y into equation (5)

Answer: Jacob’s Age = 40 Years, Son’s Age = 10 Years

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]]> Exercise 3.1 (NCERT) – Pair of Linear Equations in Two Variables, Class 10 – All Solutions https://mathemafia.com/exercise-3-1-ncert-pair-of-linear-equations-in-two-variables-class-10-all-solutions/ Sat, 03 May 2025 07:52:03 +0000 https://mathemafia.com/?p=17807 Exercise 3.1, chapter 3, Pair of Linear Equations in Two Variables, Class 10 - All questions are solved using Mathematical symbols and scalable vector graphics, and line graphs. Quality educational content is provided by the experts of Mathematics.

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Exercise 3.1 (NCERT) – Pair of Linear Equations in Two Varibales, Class 10

Chapter 3 Exercise 3.1 Class 10

Below are the Quick links for all questions of Exercise 3.1, Pair of Linear Equations in Two Variables, Class 10.

Click a link to view the solution of corresponding question.

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Below are the solutions of every question of exercise 3.1 of chapter 3, Pair of Linear Equations in Two Variables, NCERT of class 10. YouTube video tutorial of every question is also embedded along with the written solution.  

Question 1

Form the pair of linear equations in the following problems, and find their solutions

graphically.

(i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4

more than the number of boys, find the number of boys and girls who took part in

the quiz.

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Total students = 10

Let the No. of boys be x
Then the No. of girls = x + 4

Note: We have solved this question using one variable only.

(ii) 5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen.

Let the cost of one pencil be x

and the cost of one pen be y

Cost of 5 pencils and 7 pens = 50

=> 5x + 7y = 50 … (1)

Cost of 7 pencils and 5 pens = 46

=> 7x + 5y = 46 … (2)

Multiply (1) by 5 and (2) by 7 to eliminate y

Subtract (3) from (4)

Substitute x = 3 in (1)

Cost of 1 Pencil = Rs. 3
Cost of 1 Pen = Rs. 5

Question 2

On comparing the ratios a1/a2, b1/b2 and c1/c2 find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:

(i) 5x – 4y + 8 = 0

     7x + 6y – 9 = 0

Comparing the equations with standard form of Linear Equations in Two variables:

a1x + b1y + c1 = 0 &

a2x + b2y + c2 = 0

a1 = 5, b1 = -4, c1 = 8
a2 = 7,  b2 = 6, c2 = -9

Lines intersect each other at one point, Unique Solution

(ii) 9x + 3y + 12 = 0

    18x + 6y + 24 = 0

Comparing the equations with standard form of Linear Equations in Two variables:

a1x + b1y + c1 = 0 &

a2x + b2y + c2 = 0

a1 = 9, b1 = 3, c1 = 12
a2 = 18,  b2 = 6, c2 = 24

Lines are coincident, Infinite Solutions

(iii) 6x – 3y + 10 = 0

     2x – y + 9 = 0

Comparing the equations with standard form of Linear Equations in Two variables:

a1x + b1y + c1 = 0 &

a2x + b2y + c2 = 0

a1 = 6, b1 = -3, c1 = 10
a2 = 2,  b2 = -1, c2 = 9

Lines are parallel, No Solution

Question 3

On comparing the ratios a1/a2, b1/b2 and c1/c2 find out whether the following pair of linear equations are consistent, or inconsistent.

(i) 3x + 2y = 5

    2x – 3y = 7

Move the constant terms on the LHS.

3x + 2y – 5 = 0

2x – 3y – 7 = 0

Comparing the equations with standard form of Linear Equations in Two variables:

a1x + b1y + c1 = 0 &

a2x + b2y + c2 = 0

a1 = 3, b1 = 2, c1 = -5
a2 = 2,  b2 = -3, c2 = -7

Consistent, Unique Solution

(ii) 2x – 3y = 8

     4x – 6y = 9

Move the constant terms on the LHS.

2x – 3y – 8 = 0

4x – 6y – 9 = 0

Comparing the equations with standard form of Linear Equations in Two variables:

a1x + b1y + c1 = 0 &

a2x + b2y + c2 = 0

a1 = 2, b1 = -3, c1 = -8
a2 = 4,  b2 = -6, c2 = -9

Inconsistent, No Solution

(iii) 3x/2 + 5y/3 = 7

       9x – 10y = 14

Let us first remove the denominators from the equation (1)

So the equations will be:

9x + 10y – 42 = 0

9x – 10y – 14 = 0

Comparing the equations with standard form of Linear Equations in Two variables:

a1x + b1y + c1 = 0 &

a2x + b2y + c2 = 0

a1 = 9, b1 = 10, c1 = -42
a2 = 2,  b2 = -1, c2 = 9

Consistent, Uunique Solution

(iv) 5x – 3y = 11 

      – 10x + 6y = –22

Move the constant terms on the LHS.

5x – 3y – 11 = 0

–10x + 6y + 22 = 0

Comparing the equations with standard form of Linear Equations in Two variables:

a1x + b1y + c1 = 0 &

a2x + b2y + c2 = 0

a1 = 5, b1 = -3, c1 = -11
a2 = -10,  b2 = 6, c2 = 22

Consistent, Infinite Solutions

(v)  4x/3 + 2y = 8

       2x + 3y = 12

Let us first remove the denominators from the equation (1)

So the equations will be:

4x + 6y – 24 = 0

2x + 3y – 12 = 0

Comparing the equations with standard form of Linear Equations in Two variables:

a1x + b1y + c1 = 0 &

a2x + b2y + c2 = 0

a1 = 4, b1 = 6, c1 = -24
a2 = 2,  b2 = 3, c2 = -12

Consistent , Infinite solutions

Question 4

Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

(i) x + y = 5, 2x + 2y = 10

Conclusion:

The equations are equivalent
Lines are coincident
System is consistent and dependent

Consistent, Infinitely Many Solutions

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(ii) x – y = 8, 3x – 3y = 16

(1) and (3) have same LHS but different RHS

Conclusion

Lines are parallel
System is inconsistent

Inconsistent, No Solution

(iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0

Comparing the equations with standard form of Linear Equations in Two variables:

a1x + b1y + c1 = 0 &

a2x + b2y + c2 = 0

a1 = 2, b1 = 1, c1 = -6
a2 = 4,  b2 = -2, c2 = -4

Conclusion

Lines intersect each other at one point
System is consistent

Consistent, Unique Solution

(iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0

Comparing the equations with standard form of Linear Equations in Two variables:

a1x + b1y + c1 = 0 &

a2x + b2y + c2 = 0

a1 = 2, b1 = -2, c1 = -2
a2 = 4,  b2 = -4, c2 = -5

Conclusion

Lines are parallel to each other
System is inconsistent

Inconsistent, No Solution

Question 5

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is

36 m. Find the dimensions of the garden.

For Garden

Let Length = x

then Width = x + 4

Half Perimeter = 36 m

Perimeter = 2 (Length + Width)

=> Length + Width = 36

Length = x = 16 m

Width = x + 4 = 20 m

Question 6

Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

(i) intersecting lines

Two lines intersect each other if 

So any of the following equations can satisfy this condition 

3x + 2y – 8 = 0

3x + 3y – 8 = 0

11x + 11y + 11 = 0

You can write as many equations as you like.

(ii) Parallel lines

Two lines are parallel if 

The easiest way to form the second equation is using the same equation with different constant term. For example, 

2x + 3y – 1 = 0

2x + 3y – 2 = 0

2x + 3y + 3 = 0

You can write as many equations as you like.

(iii) Coincident lines

Two lines are coincident if

The easiest way to form the second equation is by multiplying the given equation with any non-zero real number. For example,

2 * ( 2x + 3y  – 8 = 0 ) = 4x + 6y – 16 = 0

3 * ( 2x + 3y  – 8 = 0 ) = 6x + 9y – 24 = 0

(-1) * ( 2x + 3y  – 8 = 0 ) = -2x – 3y + 8 = 0

You can write as many equations as you like.

Question 7

Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the

coordinates of the vertices of the triangle formed by these lines and the x-axis, and

shade the triangular region.

Graph

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Extend the Blue and Magenta lines so that these lines intersect the x-axis. Then shade the triagular region formed between these lines and x-axis. 

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]]> Class 10 | Chapter 3 | All Solutions | Pair of Linear Equations https://mathemafia.com/class-10-chapter-03-pair-of-linear-equations-all-solutions/ Thu, 16 Dec 2021 05:30:48 +0000 http://sh016.global.temp.domains/~mathemaf/?p=7141 This playlist covers all the questions, concepts and examples of chapter 1 (Pair of Linear Equations) of class 10, NCERT book. Click a thumbnail to watch the tutorial. Watch complete chapter on YouTube

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This playlist covers all the questions, concepts and examples of chapter 1 (Pair of Linear Equations) of class 10, NCERT book. Click a thumbnail to watch the tutorial. 

Watch complete chapter on YouTube

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]]> Class 10 | Chapter 3 | Pair of Linear Equations | Exercise 3.2 https://mathemafia.com/class-10-chapter-3-pair-of-linear-equations-exercise-3-2/ Mon, 05 Jul 2021 06:54:03 +0000 http://sh016.global.temp.domains/~mathemaf/?p=7109 Question 1 (i) : Form the pair of linear equations in the following problems, and find their solutions graphically. (i)  10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than…

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Question 1 (i) : Form the pair of linear equations in the following problems, and find their solutions graphically.

(i)  10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

Question 1 (ii) : Form the pair of linear equations in the following problems, and find their solutions graphically.

(ii) 5 pencils and 7 pens together cost ` 50, whereas 7 pencils and 5 pens together cost ` 46. Find the cost of one pencil and that of one pen.

Question 2: On comparing the ratios a1/a2, b1/b2 and c1/c2, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:
(i) 5x – 4y + 8 = 0, 7x + 6y – 9 = 0 (ii) 9x + 3y + 12 = 0, 18x + 6y + 24 = 0 (iii) 6x – 3y + 10 = 0, 2x – y + 9 = 0 

Question 3: On comparing the ratios a1/a2, b1/b2 and c1/c2, find out whether the following pair of linear equations are consistent, or inconsistent. (i) 3x+2y=5; 2x–3y=7 (ii) 2x–3y=8; 4x–6y=9 (iii) (3/2)x+5/3 y=7; 9x–10y=14 (iv)5x–3y=11;–10x+6y=–22 (v) (4/3)x+2y=8;2x+3y=12

Question 4: Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: (i) x+y=5, 2x+2y=10 (ii) x–y=8, 3x–3y=16 (iii) 2x+y–6=0, 4x–2y–4=0 (iv) 2x–2y–2=0, 4x–4y–5=0

Question 5: Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Question 6: Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

(i) intersecting lines (ii) parallel lines (iii) coincident lines

Question 7: Draw the graphs of the equations x–y+1=0 and 3x+2y–12=0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Class 10 | Ex: 3.1
Class 10 | Ex: 3.3

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Class 10 – Mathematics – NCERT Solutions

  1. Real Numbers
  2. Polynomials
  3. Pair of Linear Equation in Two Variables
  1. Quadratic Equations
  2. Arithmetic Progressions
  3. Triangles
  1. Coordinate Geometry
  2. Introduction to Trigonometry
  3. Some Applications of Trigonometry
    • Exercise 9.1
  4. Circles
  1. Areas Related to Circles
  2. Surface Areas and Volumes
  3. Statistics
    • Exercise 13.1
    • Exercise 13.2
    • Exercise 13.3
  4. Probability

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]]> Class 10 | Chapter 3 | Pair of Linear Equations | Exercise 3.1 https://mathemafia.com/class-10-chapter-3-pair-of-linear-equations-exercise-3-1/ Mon, 05 Jul 2021 06:49:02 +0000 http://sh016.global.temp.domains/~mathemaf/?p=7104 Question 1: Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this…

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Question 1: Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Question 2: The coach of a cricket team buys 3 bats and 6 balls for Rs. 3900. Later, she buys another bat and 3 more balls of the same kind for Rs. 1300. Represent this situation algebraically and geometrically.

Question 3: The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs. 300. Represent the situation algebraically and geometrically.

Class 10 | Chapter 3 | All Examples
Class 10 | Ex: 3.2

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Saiba

An Excellent Math Teacher

Sunil Sir has been an excellent math teacher for Saiba. His teaching methods are highly informative, engaging, and motivational which have greatly strengthened Saiba’s understanding of maths concepts. He consistently provides support beyond the classroom and has played an important role in improving Saiba’s problem-solving skills and preparation for math competitions. His dedication and professionalism make him an outstanding educator. Saiba is thankful for his continued support and positive influence.

 

– Saiba’s Parents (USA)

Amazing Math Coach

Sunil is an amazing math coach! My son Rishi loves to learn from him. He makes learning fun and engages Rishi. Sunil is also very patient with kids and understands my son’s learning methods and teaches accordingly with positive reinforcement. Very thankful to him!

 

– Rishi’s Parents (USA)

Rishi (USA Student)

Unique, Patient and Good Mentor

Sunil sir has a unique way of explaining complex concepts, making them simple and understandable. You are very patient and always encourages me to ask queries as many times until the concept is clearer. You are a great person besides being a good mentor and always in a light mood and never gets frustrated for anything. My grades have immensely improved and I am much more confident in maths now.

 

Also, your videos on Mathemafia youtube channel are very informative.

 

– Lakshay (USA)

WhatsApp for 1-1 Classes

❇️ ❇️ M️aster List – All Maths Formulas, Class 10 ❇️ ❇️

Class 10 – Mathematics – NCERT Solutions

  1. Real Numbers
  2. Polynomials
  3. Pair of Linear Equation in Two Variables
  1. Quadratic Equations
  2. Arithmetic Progressions
  3. Triangles
  1. Coordinate Geometry
  2. Introduction to Trigonometry
  3. Some Applications of Trigonometry
    • Exercise 9.1
  4. Circles
  1. Areas Related to Circles
  2. Surface Areas and Volumes
  3. Statistics
    • Exercise 13.1
    • Exercise 13.2
    • Exercise 13.3
  4. Probability

Super Cool Stuff

The post Class 10 | Chapter 3 | Pair of Linear Equations | Exercise 3.1 appeared first on Mathemafia.

]]> Class 10 | Chapter 3 | Pair of Linear Equations | Examples https://mathemafia.com/class-10-chapter-3-pair-of-linear-equations-examples/ Mon, 05 Jul 2021 06:36:37 +0000 http://sh016.global.temp.domains/~mathemaf/?p=7096 Example 1: Let us take the example given in Section 3.1. Akhila goes to a fair with ` 20 and wants to have rides on the Giant Wheel and play Hoopla. Represent this situation algebraically and graphically (geometrically). Example 2:…

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Example 1: Let us take the example given in Section 3.1. Akhila goes to a fair with ` 20 and wants to have rides on the Giant Wheel and play Hoopla. Represent this situation algebraically and graphically (geometrically).

Example 2: Romila went to a stationery shop and purchased 2 pencils and 3 erasers for Rs. 9. Her friend Sonali saw the new variety of pencils and erasers with Romila, and she also bought 4 pencils and 6 erasers of the same kind for Rs. 18. Represent this situation algebraically and graphically.

Example 3: Two rails are represented by the equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Represent this situation geometrically.

Example 4: Check graphically whether the pair of equations

x + 3y = 6 and 2x – 3y = 12

is consistent. If so, solve them graphically.

Example 5: Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions:

5x – 8y + 1 = 0, 3x – 24/5 y + 3/5 = 0

Example 6: Champa went to a ‘Sale’ to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, “The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased”. Help her friends to find how many pants and skirts Champa bought.

Example 7: Solve the following pair of equations by substitution method: 7x – 15y = 2, x + 2y = 3

Example 8: Solve Q.1 of Exercise 3.1 by the method of substitution.

Example 9: Let us consider Example 2 in Section 3.3, i.e., the cost of 2 pencils and 3 erasers is Rs. 9 and the cost of 4 pencils and 6 erasers is `Rs.18. Find the cost of each pencil and each eraser.

Example 10: Let us consider the Example 3 of Section 3.2. Will the rails cross each other?

Class 10 | Chapter 3 | Theorems & Concepts
Class 10 | Ex: 3.1

Testimonials

Saiba

An Excellent Math Teacher

Sunil Sir has been an excellent math teacher for Saiba. His teaching methods are highly informative, engaging, and motivational which have greatly strengthened Saiba’s understanding of maths concepts. He consistently provides support beyond the classroom and has played an important role in improving Saiba’s problem-solving skills and preparation for math competitions. His dedication and professionalism make him an outstanding educator. Saiba is thankful for his continued support and positive influence.

 

– Saiba’s Parents (USA)

Amazing Math Coach

Sunil is an amazing math coach! My son Rishi loves to learn from him. He makes learning fun and engages Rishi. Sunil is also very patient with kids and understands my son’s learning methods and teaches accordingly with positive reinforcement. Very thankful to him!

 

– Rishi’s Parents (USA)

Rishi (USA Student)

Unique, Patient and Good Mentor

Sunil sir has a unique way of explaining complex concepts, making them simple and understandable. You are very patient and always encourages me to ask queries as many times until the concept is clearer. You are a great person besides being a good mentor and always in a light mood and never gets frustrated for anything. My grades have immensely improved and I am much more confident in maths now.

 

Also, your videos on Mathemafia youtube channel are very informative.

 

– Lakshay (USA)

WhatsApp for 1-1 Classes

❇️ ❇️ M️aster List – All Maths Formulas, Class 10 ❇️ ❇️

Class 10 – Mathematics – NCERT Solutions

  1. Real Numbers
  2. Polynomials
  3. Pair of Linear Equation in Two Variables
  1. Quadratic Equations
  2. Arithmetic Progressions
  3. Triangles
  1. Coordinate Geometry
  2. Introduction to Trigonometry
  3. Some Applications of Trigonometry
    • Exercise 9.1
  4. Circles
  1. Areas Related to Circles
  2. Surface Areas and Volumes
  3. Statistics
    • Exercise 13.1
    • Exercise 13.2
    • Exercise 13.3
  4. Probability

Super Cool Stuff

The post Class 10 | Chapter 3 | Pair of Linear Equations | Examples appeared first on Mathemafia.

]]> Class 10 | Chapter 3 | Pair of Linear Equations | Theorems & Concepts https://mathemafia.com/class-10-chapter-3-pair-of-linear-equations-theorems-concepts/ Mon, 05 Jul 2021 06:24:19 +0000 http://sh016.global.temp.domains/~mathemaf/?p=7090 Concept: In this tutorial, you will be introduced to the pair of Linear equations and their graphical representation. The concepts have been explained with the help of very easy examples. Concept: The ratio of the coefficients of a pair of…

The post Class 10 | Chapter 3 | Pair of Linear Equations | Theorems & Concepts appeared first on Mathemafia.

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Concept: In this tutorial, you will be introduced to the pair of Linear equations and their graphical representation. The concepts have been explained with the help of very easy examples.

Concept: The ratio of the coefficients of a pair of linear equations in two variables can be used to quickly identify whether the pair has a uniques solution, infinite solutions or no solution at all. This also means that the ratios can be used to quickly identify whether the lines are intersection, coincident or parallel.

Class 10 | Home
Class 10 | Chapter 3 | All Examples

Testimonials

Saiba

An Excellent Math Teacher

Sunil Sir has been an excellent math teacher for Saiba. His teaching methods are highly informative, engaging, and motivational which have greatly strengthened Saiba’s understanding of maths concepts. He consistently provides support beyond the classroom and has played an important role in improving Saiba’s problem-solving skills and preparation for math competitions. His dedication and professionalism make him an outstanding educator. Saiba is thankful for his continued support and positive influence.

 

– Saiba’s Parents (USA)

Amazing Math Coach

Sunil is an amazing math coach! My son Rishi loves to learn from him. He makes learning fun and engages Rishi. Sunil is also very patient with kids and understands my son’s learning methods and teaches accordingly with positive reinforcement. Very thankful to him!

 

– Rishi’s Parents (USA)

Rishi (USA Student)

Unique, Patient and Good Mentor

Sunil sir has a unique way of explaining complex concepts, making them simple and understandable. You are very patient and always encourages me to ask queries as many times until the concept is clearer. You are a great person besides being a good mentor and always in a light mood and never gets frustrated for anything. My grades have immensely improved and I am much more confident in maths now.

 

Also, your videos on Mathemafia youtube channel are very informative.

 

– Lakshay (USA)

WhatsApp for 1-1 Classes

❇️ ❇️ M️aster List – All Maths Formulas, Class 10 ❇️ ❇️

Class 10 – Mathematics – NCERT Solutions

  1. Real Numbers
  2. Polynomials
  3. Pair of Linear Equation in Two Variables
  1. Quadratic Equations
  2. Arithmetic Progressions
  3. Triangles
  1. Coordinate Geometry
  2. Introduction to Trigonometry
  3. Some Applications of Trigonometry
    • Exercise 9.1
  4. Circles
  1. Areas Related to Circles
  2. Surface Areas and Volumes
  3. Statistics
    • Exercise 13.1
    • Exercise 13.2
    • Exercise 13.3
  4. Probability

Super Cool Stuff

The post Class 10 | Chapter 3 | Pair of Linear Equations | Theorems & Concepts appeared first on Mathemafia.

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