Class 10 Maths · Chapter 3

Pair of Linear Equations in Two Variables

81 Class 10 Maths questions on Pair of Linear Equations in Two Variables from the NCERT textbook, NCERT Exemplar and CBSE board papers 2026, each with its answer and a step-by-step solution.

NCERT exercises

Exercise 3.1 (7) Exercise 3.2 (3) Exercise 3.3 (0)

NCERT Exemplar exercises

Exercise 3.1 (13) Exercise 3.2 (6) Exercise 3.3 (22) Exercise 3.4 (0)

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 3 of 5

Q41 Exemplar · Exercise 3.3

Draw the graph of the pair of equations $2 x + y = 4$ and $2 x - y = 4$ . Write the vertices of the triangle formed by these lines and the $y$ -axis. Also find the area of this triangle.

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Vertices: $(0, 4)$ , $(0, - 4)$ , $(2, 0)$ ; Area $= 8$ square units.

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Q42 Exemplar · Exercise 3.3

Write an equation of a line passing through the point representing solution of the pair of linear equations $x + y = 2$ and $2 x - y = 1$ . How many such lines can we find?

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The solution point is $(1, 1)$ ; one line through it is $y = x$ . Infinitely many such lines can be found.

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Q43 Exemplar · Exercise 3.3

If $x + 1$ is a factor of $2 x^{3} + a x^{2} + 2 b x + 1$ , then find the values of $a$ and $b$ given that $2 a - 3 b = 4$ .

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$a = 5$ and $b = 2$ .

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Q44 Exemplar · Exercise 3.3

The angles of a triangle are $x$ , $y$ and $4 0^{\circ}$ . The difference between the two angles $x$ and $y$ is $3 0^{\circ}$ . Find $x$ and $y$ .

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$x = 8 5^{\circ}$ and $y = 5 5^{\circ}$ .

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Q45 Exemplar · Exercise 3.3

Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?

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Salim is 38 years old and his daughter is 14 years old now.

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Q46 Exemplar · Exercise 3.3

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

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The father's present age is $40$ years.

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Q47 Exemplar · Exercise 3.3

Two numbers are in the ratio $5 : 6$ . If $8$ is subtracted from each of the numbers, the ratio becomes $4 : 5$ . Find the numbers.

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The numbers are $40$ and $48$ .

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Q48 Exemplar · Exercise 3.3

There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to B. But if 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in the two halls.

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Hall A has $100$ students and hall B has $80$ students.

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Q49 Exemplar · Exercise 3.3

A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs 22 for a book kept for six days, while Anand paid Rs 16 for the book kept for four days. Find the fixed charges and the charge for each extra day.

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Fixed charge $=$ Rs $10$ (for the first two days); charge per extra day $=$ Rs $3$ .

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Q50 Exemplar · Exercise 3.3

In a competitive examination, one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

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Jayanti answered $100$ questions correctly.

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Q51 Exemplar · Exercise 3.3

The angles of a cyclic quadrilateral ABCD are $∠ A = (6 x + 10)^{\circ}$ , $∠ B = (5 x)^{\circ}$ , $∠ C = (x + y)^{\circ}$ , $∠ D = (3 y - 10)^{\circ}$ . Find $x$ and $y$ , and hence the values of the four angles.

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$x = 20$ , $y = 30$ ; $∠ A = 13 0^{\circ}$ , $∠ B = 10 0^{\circ}$ , $∠ C = 5 0^{\circ}$ , $∠ D = 8 0^{\circ}$ .

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Q52 CBSE 2026
The value of $k$ for which the pair of linear equations $k x - 3 y = 5$ , $4 x - 6 y = 10$ has infinitely many solutions, is:
1. (a) $4$
2. (b) $3$
3. (c) $2$
4. (d) $1$
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(c) $2$

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Q53 CBSE 2026
If pair of linear equations given by $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ has infinitely many solutions, then which of the following is definitely true?
1. (a) $\frac{a _{1}}{a _{2}} = \frac{c _{2}}{c _{1}}$
2. (b) $a_{1} a_{2} \neq = b_{1} b_{2}$
3. (c) $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$
4. (d) $a_{1} b_{2} = a_{2} b_{1}$
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(d) $a_{1} b_{2} = a_{2} b_{1}$

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Q54 CBSE 2026
Which of the following system of equations has a unique solution ?
1. (a) $x = 0, x = 1$
2. (b) $x + y = 0, 2 x + 2 y = 0$
3. (c) $x + y = 2, x - y = 3$
4. (d) $x + y = 5, x + y = 10$
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(c) $x + y = 2, x - y = 3$

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Q55 CBSE 2026
The system of equations $2 x + k y = 4$ and $3 x - 6 y = 6$ has infinitely many solutions, if :
1. (a) $k \neq = 4$
2. (b) $k = 4$
3. (c) $k = - 4$
4. (d)No value of $k$
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(c) $k = - 4$

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Q56 CBSE 2026
The system of linear equations $p x + q y = r$ and $p_{1} x + q_{1} y = r_{1}$ has a unique solution, if :
1. (a) $pq \neq = p_{1} q_{1}$
2. (b) $p p_{1} \neq = q q_{1}$
3. (c) $p q_{1} \neq = q p_{1}$
4. (d) $pq r \neq = p_{1} q_{1} r_{1}$
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(c) $p q_{1} \neq = q p_{1}$

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Q57 CBSE 2026
If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has :
1. (a)a unique solution
2. (b)two solutions
3. (c)no solution
4. (d)an infinite number of solutions
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(d) an infinite number of solutions

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Q58 CBSE 2026
If the pair of linear equations : $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ is consistent and dependent, then
1. (a) $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$
2. (b) $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$
3. (c) $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$
4. (d) $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$
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(d) $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$

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Q59 CBSE 2026
Equation of another line parallel to the line represented by $2 x - 6 y = 7$ is :
1. (a) $y = 3 x - 7$
2. (b) $2 x = 9 - 6 y$
3. (c) $x - 3 y = 7$
4. (d) $x = \frac{7}{2} - 3 y$
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(c) $x - 3 y = 7$

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Q60 CBSE 2026
The value of $k$ for which the system of linear equations $\frac{x}{2} + \frac{y}{3} = 5$ and $2 x + k y = 7$ is inconsistent, is
1. (a) $\frac{3}{4}$
2. (b) $\frac{4}{3}$
3. (c) $\frac{1}{3}$
4. (d) $3$
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(b) $\frac{4}{3}$

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