CBSE BOARD PYQS · CHAPTER 03

Pair of Linear Equations in Two Variables
CBSE Most Repeated PYQs

Solve official CBSE Previous Year Board Questions (2015-2024) for Pair of Linear Equations in Two Variables. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.

Q1CBSE 2024, 2020MCQ

1 Mark

The pair of equations x + 2y + 5 = 0 and -3x - 6y + 1 = 0 has:

Q2CBSE 2023, 2019MCQ

1 Mark

If a pair of linear equations is consistent, then the lines will be:

Q3CBSE 2022, 2018MCQ

1 Mark

Value of k for which 3x - y + 8 = 0 and 6x - ky + 16 = 0 represent coincident lines is:

Q4CBSE 2024, 2021MCQ

1 Mark

The solution of equations x + y = 7 and 2x - 3y = 9 is:

Q5CBSE 2023, 2017Assertion-Reason

1 Mark

Assertion (A): System of equations 2x + 3y = 7 and 4x + 6y = 14 has infinitely many solutions. Reason (R): If a₁/a₂ = b₁/b₂ = c₁/c₂, system of equations is dependent and consistent.

Q6CBSE 2020, 2016Assertion-Reason

1 Mark

Assertion (A): Lines x = 2 and y = 3 intersect at point (2, 3). Reason (R): Line x = a is parallel to y-axis and y = b is parallel to x-axis.

Q7CBSE 2024, 2020Short Answer

2 Marks

Solve for x and y: x + y = 14, x - y = 4.

Q8CBSE 2023, 2019Short Answer

2 Marks

Solve by elimination: 2x + 3y = 11 and 2x - 4y = -24.

Q9CBSE 2022, 2018Short Answer

2 Marks

Find condition for unique solution of 4x + py + 8 = 0 and 2x + 2y + 2 = 0.

Q10CBSE 2024, 2021Short Answer

2 Marks

Find k if kx + 3y = k - 3 and 12x + ky = k have infinitely many solutions.

Q11CBSE 2023, 2017Short Answer

2 Marks

Sum of digits of two-digit number is 9. 9 times number is twice reversed number. Find number.

Q12CBSE 2020, 2016Long Answer

3 Marks

Solve graphically: 2x + 3y = 12 and x - y = 1. Find y-axis triangle vertices.

Q13CBSE 2024, 2020Long Answer

3 Marks

Fraction becomes 9/11 if 2 added to num & den, 5/6 if 3 added. Find fraction.

Q14CBSE 2023, 2019Long Answer

3 Marks

Five years ago Nuri was thrice as old as Sonu. Ten years later Nuri will be twice as old. Find ages.

Q15CBSE 2022, 2018Long Answer

3 Marks

Meena withdrew ₹2000 in ₹50 and ₹100 notes (total 25 notes). Find count of each note.

Q16CBSE 2024, 2021Case Study

4 Marks

Case Study Scenario: A test has 1-mark and 2-mark questions. Total questions = 40, total marks = 60. Question: Find number of 1-mark and 2-mark questions.

Q17CBSE 2023, 2017Case Study

4 Marks

Case Study Scenario: A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it goes 40 km upstream & 55 km downstream. Question: Find speed of boat in still water and speed of stream.

Q18CBSE Official Board PYQPYQ

5 Marks

2 women & 5 men finish work in 4 days, 3 women & 6 men in 3 days. Find time for 1 woman alone.

Q19CBSE Official Board PYQPYQ

5 Marks

If 217x + 131y = 913 and 131x + 217y = 827, find x + y.

Q20CBSE Official Board PYQPYQ

5 Marks

Pair of Linear Equations in Two Variables CBSE Most Repeated PYQs

The pair of equations x + 2y + 5 = 0 and -3x - 6y + 1 = 0 has:

If a pair of linear equations is consistent, then the lines will be:

Value of k for which 3x - y + 8 = 0 and 6x - ky + 16 = 0 represent coincident lines is:

The solution of equations x + y = 7 and 2x - 3y = 9 is:

Assertion (A): System of equations 2x + 3y = 7 and 4x + 6y = 14 has infinitely many solutions. Reason (R): If a₁/a₂ = b₁/b₂ = c₁/c₂, system of equations is dependent and consistent.

Assertion (A): Lines x = 2 and y = 3 intersect at point (2, 3). Reason (R): Line x = a is parallel to y-axis and y = b is parallel to x-axis.

Solve for x and y: x + y = 14, x - y = 4.

Solve by elimination: 2x + 3y = 11 and 2x - 4y = -24.

Find condition for unique solution of 4x + py + 8 = 0 and 2x + 2y + 2 = 0.

Find k if kx + 3y = k - 3 and 12x + ky = k have infinitely many solutions.

Sum of digits of two-digit number is 9. 9 times number is twice reversed number. Find number.

Solve graphically: 2x + 3y = 12 and x - y = 1. Find y-axis triangle vertices.

Fraction becomes 9/11 if 2 added to num & den, 5/6 if 3 added. Find fraction.

Five years ago Nuri was thrice as old as Sonu. Ten years later Nuri will be twice as old. Find ages.

Meena withdrew ₹2000 in ₹50 and ₹100 notes (total 25 notes). Find count of each note.

Case Study Scenario: A test has 1-mark and 2-mark questions. Total questions = 40, total marks = 60. Question: Find number of 1-mark and 2-mark questions.

Case Study Scenario: A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it goes 40 km upstream & 55 km downstream. Question: Find speed of boat in still water and speed of stream.

2 women & 5 men finish work in 4 days, 3 women & 6 men in 3 days. Find time for 1 woman alone.

If 217x + 131y = 913 and 131x + 217y = 827, find x + y.

Solve for x and y: ax + by = a - b, bx - ay = a + b.

Pair of Linear Equations in Two Variables
CBSE Most Repeated PYQs