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.
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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.
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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.
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Class 10 – Mathematics – NCERT Solutions
- Real Numbers
- Polynomials
- Pair of Linear Equation in Two Variables
- Quadratic Equations
- Arithmetic Progressions
- Triangles
- Exercise 6.1
- Exercise 6.2
- Exercise 6.3
- Coordinate Geometry
- Introduction to Trigonometry
- Some Applications of Trigonometry
- Exercise 9.1
- Circles
- Areas Related to Circles
- Surface Areas and Volumes
- Exercise 12.1
- Exercise 12.2
- Statistics
- Exercise 13.1
- Exercise 13.2
- Exercise 13.3
- Probability
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- Calculators
- Quadratic Equation Calculator – Solve any Equation
- Super Concepts
