Class 10 Maths · Chapter 3

Pair of Linear Equations in Two Variables

96 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 5 of 5

1. Q81 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 →
2. Q82 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 →
3. Q83 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 →
4. Q84 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 →
5. Q85 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 →
6. Q86 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 →
7. Q87 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 →
8. Q88 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 →
9. Q89 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 →
10. Q90 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 →
11. Q91 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 →
12. Q92 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 →
13. Q93 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 →
14. Q94 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 →
15. Q95 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 →
16. Q96 CBSE 2026
    Seema daily goes to a park ​to exercise on machines available there. When Seema spent $15$ minutes on exercise bicycle and $30$ minutes on double cross walker, ​she received a message of burning $435$ ​calories on her fitness watch. ​When she spent $30$ minutes on ​exercise bicycle and $40$ minutes on ​double cross walker, she received a message of burning $690$ calories. To find the number of calories ​burned per minute on each ​machine, answer the following:

    1. (i)Represent the above situation in terms of a pair of linear equations in two variables.
    2. (ii)Show that the equations have unique solution.
    3. (iii)(a) Solve both equations to find the values of the variables using elimination method. OR (b) Solve both equations to find the values of the variables using substitution method.
    Show answer

    (i) $15x+30y=435$ and $30x+40y=690$ (equivalently $x+2y=29$ and $3x+4y=69$), where $x$ and $y$ are the calories burned per minute on the exercise bicycle and the double cross walker. (ii) Since $\frac{a_1}{a_2}=\frac{1}{3}\ne \frac{1}{2}=\frac{b_1}{b_2}$, the pair has a unique solution. (iii) $x=11$ and $y=9$, i.e. $11$ calories per minute on the exercise bicycle and $9$ calories per minute on the double cross walker.

    Step-by-step solution →