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.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 4 of 5

1. Q61 CBSE 2026
   The number ​of solutions of the ​system of ​equations ​given ​by $x=-2$ ​and $y=2$ ​is :

   1. (a)$0$
   2. (b)$1$
   3. (c)$2$
   4. (d)infinite
   Show answer

   (b) $1$

   Step-by-step solution →
2. Q62 CBSE 2026
   The sum of ​the age (in years) of a father and three times the age of his daughter is $59$. ​If the age of the father ​is $x$ years ​and that ​of ​his daughter ​is $y$ years, the equation ​representing the given information is :

   1. (a)$3x+y=59$
   2. (b)$x+y=59$
   3. (c)$x+3y=59$
   4. (d)$x+y=56$
   Show answer

   (c) $x+3y=59$

   Step-by-step solution →
3. Q63 CBSE 2026
   The system ​of ​equations $x=2$ ​and $x=3$ has ​:

   1. (a)unique solution $(2,3)$
   2. (b)two solutions $(2,0)$ and $(3,0)$
   3. (c)no solution
   4. (d)infinitely many solutions
   Show answer

   (c) no solution

   Step-by-step solution →
4. Q64 CBSE 2026
   In the question below, a ​statement of ​Assertion ​(A) ​is ​followed by a ​statement of ​Reason ​(R). Choose the correct option.

   Assertion (A): The system of linear equations $3x-5y+7=0$ and $-6x+10y+14=0$ is inconsistent.

   Reason (R): When two linear equations do not have a unique solution, they always represent parallel lines.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true, but Reason (R) is false.
   4. (d)Assertion (A) is false, but Reason (R) is true.
   Show answer

   (c) Assertion (A) is true, but Reason (R) is false.

   Step-by-step solution →
5. Q65 CBSE 2026
   In a class ​test, Veer scored $6$ more ​than twice as many marks as ​Kevin scored. If one of them ​had scored $4$ more marks, their total score ​would have been $40$. Find the marks obtained by Veer and Kevin.
   Show answer

   Veer obtained $26$ marks and Kevin obtained $10$ marks.

   Step-by-step solution →
6. Q66 CBSE 2026
   Solve ​the ​linear equations $3x+y=14$ ​and $y=2$ graphically.
   Show answer

   $x=4$ and $y=2$ (the lines meet at the point $(4,2)$).

   Step-by-step solution →
7. Q67 CBSE 2026
   Solve ​the following ​pair ​of linear ​equations: $31x+43y-117=0$; $43x+31y=105$.
   Show answer

   $x=1$ and $y=2$.

   Step-by-step solution →
8. Q68 CBSE 2026
   Solve ​the following system ​of ​equations graphically : $x+3y=6$ and $2x-3y=12$ Also, find ​the area ​of the triangle formed by the lines $x+3y=6$, $x=0$ and $y=0$.
   Show answer

   The lines meet at $(6,0)$, so the solution is $x=6$, $y=0$; the triangle formed by $x+3y=6$ with the lines $x=0$ and $y=0$ has area $6$ square units.

   Step-by-step solution →
9. Q69 CBSE 2026
   Prove ​that the ​system of equations given as $2x-3y=7$ and $4x+ky=9$, is inconsistent ​for $k=-6$. ​Also, ​obtain the solution of the ​system of ​equations, ​if $k=-1$.
   Show answer

   For $k=-6$ : $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{1}{2}$ but $\frac{c_1}{c_2}=\frac{7}{9}$, so the lines are parallel and the system is inconsistent; for $k=-1$ the solution is $x=2$, $y=-1$.

   Step-by-step solution →
10. Q70 CBSE 2026
    When $1$ ​is ​subtracted from the numerator ​and $2$ is added to the denominator ​of a fraction, ​it becomes $\frac{1}{2}$. When $7$ ​is subtracted from the numerator and $2$ is subtracted from the denominator, the fraction becomes $\frac{1}{3}$. Find the fraction.
    Show answer

    The fraction is $\frac{15}{26}$.

    Step-by-step solution →
11. Q71 CBSE 2026
    One ​of ​the supplementary angles exceeds ​the other ​by $120^{\circ }$. Express the given information as a ​system of linear equations in two variables. Hence, find ​the measure of both the angles.
    Show answer

    The system is $x+y=180$, $x-y=120$, giving angles of $150^{\circ }$ and $30^{\circ }$.

    Step-by-step solution →
12. Q72 CBSE 2026
    Solve ​the ​system ​of linear ​equations $x=4$ and $3x-2y=6$ ​graphically.
    Show answer

    The two lines intersect at $(4,3)$, so the solution is $x=4$ and $y=3$.

    Step-by-step solution →
13. Q73 CBSE 2026
    Determine graphically, the ​coordinates of vertices of ​a ​triangle ​whose ​equations are $2x-3y+6=0$; $2x+3y-18=0$ and $x=0$. Also, find the ​area of ​this triangle.
    Show answer

    The vertices of the triangle are $(0,2)$, $(0,6)$ and $(3,4)$, and the area of the triangle is $6$ square units.

    Step-by-step solution →
14. Q74 CBSE 2026
    Aarush ​bought $2$ pencils and $3$ ​chocolates ​for ₹ $11$ and ​Tanish bought $1$ pencil and $2$ chocolates for ₹ $7$ from the same shop. Represent this ​situation in ​the form of a pair of ​linear equations. Find the price of $1$ pencil ​and $1$ chocolate, graphically.
    Show answer

    The pair of linear equations is $2x+3y=11$ and $x+2y=7$; the two lines intersect at $(1,3)$, so the price of $1$ pencil is ₹ $1$ and the price of $1$ chocolate is ₹ $3$.

    Step-by-step solution →
15. Q75 CBSE 2026
    A fraction ​becomes $\frac{5}{6}$ ​when $3$ is added ​to both the numerator and the denominator. If $2$ is added to both the numerator and the denominator, the fraction becomes $\frac{9}{11}$. Express ​the ​given information algebraically as ​a system of linear equations in two variables. Hence, find the original fraction.
    Show answer

    The given information is represented by the system $6x-5y=-3$ and $11x-9y=-4$, where $x$ is the numerator and $y$ is the denominator. Solving this pair gives $x=7$ and $y=9$, so the original fraction is $\frac{7}{9}$.

    Step-by-step solution →
16. Q76 CBSE 2026
    The sum ​of numerator and denominator of ​a fraction is $4$ less ​than twice the ​denominator. ​If each of the numerator and ​denominator is decreased by $1$, ​the fraction becomes $\frac{1}{3}$. Find the fraction.
    Show answer

    The required fraction is $\frac{3}{7}$.

    Step-by-step solution →
17. Q77 CBSE 2026
    Solve ​the ​following system ​of ​equations graphically : $x-2y=3$, $3x-8y=7$
    Show answer

    The lines intersect at $(5,1)$, so $x=5$ and $y=1$.

    Step-by-step solution →
18. Q78 CBSE 2026
    Five years ago, Adil was thrice ​as old as Bharat. Ten ​years later Adil shall be twice as old as Bharat. To know the present ages ​of Adil and Bharat :

    1. (i)form the ​linear ​equations ​representing the above information.
    2. (ii)show that the ​system of equations is consistent with ​unique solution.
    3. (iii)find the present ages of Adil and Bharat.
    Show answer

    (i) The equations are $x-3y=-10$ and $x-2y=10$, where $x$ and $y$ are the present ages (in years) of Adil and Bharat. (ii) Since $\frac{a_1}{a_2}=1\ne \frac{3}{2}=\frac{b_1}{b_2}$, the lines intersect, so the system is consistent with a unique solution. (iii) Adil's present age is $50$ years and Bharat's present age is $20$ years.

    Step-by-step solution →
19. Q79 CBSE 2026
    The difference between two numbers ​is $12$. The greater number is $6$ ​less than twice the smaller one.

    1. (i)Representing ​the above ​situation, frame ​two linear equations in two variables.
    2. (ii)​Show that the ​equations have unique solution.
    3. (iii)Solve the equations and hence ​find the numbers.
    Show answer

    (i) The equations are $x-y=12$ and $x-2y=-6$ (where $x$ is the greater and $y$ the smaller number); (ii) since $\frac{a_1}{a_2}=1\ne \frac{1}{2}=\frac{b_1}{b_2}$, the pair has a unique solution; (iii) the numbers are $30$ and $18$.

    Step-by-step solution →
20. Q80 CBSE 2026
    Solve ​the following ​equations ​graphically ​: $x+y=7$ and $2x-5y=7$.
    Show answer

    The lines intersect at $(6,1)$, so $x=6$ and $y=1$.

    Step-by-step solution →