Pair of Linear Equations in Two Variables

CBSE Class 10 · Mathematics · 33 past questions

These are the board's own papers. 179 more board questions reprinted in the books we use in class are for signed-in students: sign in.

Q1 2026

Equation of another line parallel to the line represented by $2x - 6y = 7$ is…
Q2 2026

Solve the following system of equations graphically…
Q3 2026

Solve the system of linear equations : $x = 4$ and $3x - 2y = 6$ graphically.
Q4 2026

The value of k for which the system of linear equations $\frac{x}{2}+\frac{y}{3}=5$ and $2x + ky = 7$ is…
Q5 2026

In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4…
Q6 Sample paper 2026-27

Tarun correctly solved a pair of linear equations in two variables and found their only point of intersection…
Q7 Sample paper 2026-27

A student entrepreneur started a company that manufactures sanitizers in two sizes – small and large. The…
Q8 2025

The line represented by the equation $x - y = 0$ is…
Q9 2025

A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests… (with a figure)
Q10 2025

The value of 'k' for which the system of linear equations 6x + y = 3k and 36x + 6y = 3 have infinitely many…
Q11 2025

If $x = 1$ and $y = 2$ is a solution of the pair of linear equations $2x - 3y + a = 0$ and $2x + 3y - b = 0$…
Q12 2025

Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of 8% per…
Q13 2025 (Basic)

Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…
Q14 2025 (Basic)

Solve the following system of equations for x and y…
Q15 2025 (Basic)

Solve the following system of equations graphically…
Q16 2024

The pair of linear equations $x + 2y + 5 = 0$ and $-3x = 6y - 1$ has
Q17 2024

If $2x + y = 13$ and $4x - y = 17$, find the value of $(x - y)$.
Q18 2024

Solve the following system of linear equations graphically…
Q19 2024

The value of k for which the system of equations $3x - y + 8 = 0$ and $6x - ky + 16 = 0$ has infinitely many…
Q20 2024

Using graphical method, solve the following system of equations…
Q21 2024

Solve the following system of linear equations 7x – 2y = 5 and 8x + 7y = 15 and verify your answer.
Q22 2024

Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma.…
Q23 2024 (Basic)

The value of $k$ for which the pair of linear equations $5x+2y-7=0$ and $2x+ky+1=0$ don't have a solution, is…
Q24 2024 (Basic)

The greater of two supplementary angles exceeds the smaller by $18°$. Find measures of these two angles.
Q25 2023

If the pair of equations $3x - y + 8 = 0$ and $6x - ry + 16 = 0$ represent coincident lines, then the value…
Q26 2023

The pair of equations $x = a$ and $y = b$ graphically represents lines which are…
Q27 2023

If the system of linear equations…
Q28 2023

The pair of linear equations $2x = 5y + 6$ and $15y = 6x - 18$ represents two lines which are…
Q29 2023

The value of k for which the pair of equations $kx = y + 2$ and $6x = 2y + 3$ has infinitely many solutions…
Q30 2023

Solve the pair of equations $x = 3$ and $y = -4$ graphically.
Q31 2023

Half of the difference between two numbers is 2. The sum of the greater number and twice the smaller number…
Q32 2023 (Basic)

The larger of two supplementary angles exceeds the smaller by 18 degrees. What is the measure of larger angle…
Q33 2023 (Basic)

Solve for $x$ and $y$ : $x + y = 6$, $2x - 3y = 4$.