solutions of equations Archives – Mathemafia http://sh016.global.temp.domains/~mathemaf/tag/solutions-of-equations/ Mathematics is like music - Enjoy it!!! Fri, 17 Dec 2021 14:40:58 +0000 en-US hourly 1 https://wordpress.org/?v=7.0 https://mathemafia.com/wp-content/uploads/2020/08/cropped-M__Logo__SM-1-32x32.png solutions of equations Archives – Mathemafia http://sh016.global.temp.domains/~mathemaf/tag/solutions-of-equations/ 32 32 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

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

]]>

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

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

]]> 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…

The post Class 10 | Chapter 3 | Pair of Linear Equations | Exercise 3.2 appeared first on Mathemafia.

]]>

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

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 | Exercise 3.2 appeared first on Mathemafia.

]]> 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…

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

]]>

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

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 | 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:…

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

]]>

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.

]]>

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.

]]>