LIWA

Pair of Linear Equations in Two Variables

CBSE Class 10 · Maths · Chapter 3

Past board exam questions

CBSE 2027 sample paper · 1 mark

For what value of p does the pair of Linear equations 4x + py + 8 = 0 and 2x + 2y + 2 = 0 has a unique solution

  1. p = 4 only
  2. p = 2 only
  3. p ≠ 4
  4. p ≠ 2
Show answer
p ≠ 4

CBSE 2027 sample paper · 1 mark

Tarun correctly solved a pair of linear equations in two variables and found their only point of intersection as (5, – 1). One of the lines was x – y = 6. Which of the following could have been the other line? I: 3x – 3y = 18 II: 2x – 3y = 13 III: 2x – 3y = 16

  1. I only
  2. II only
  3. I and II
  4. II and III
Show answer
II only

CBSE 2027 sample paper · 1 mark

The sum of the numerator and denominator of a fraction is 11. If the denominator is increased by 1, the fraction becomes (1)/(2), then the fraction is

  1. (2)/(9)
  2. (3)/(8)
  3. (4)/(7)
  4. (5)/(6)
Show answer
(4)/(7)

CBSE 2027 sample paper · 3 marks

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Show answer
Let the ten's digit be x and the unit's digit be y. Number = 10x + y; reversed number = 10y + x. x + y = 9 ...(1) 9(10x + y) = 2(10y + x) ⇒ 88x = 11y ⇒ y = 8x ...(2) From (1) and (2): 9x = 9 ⇒ x = 1, y = 8. Required number = 18.

CBSE 2027 sample paper · 4 marks

A student entrepreneur started a company that manufactures sanitizers in two sizes – small and large. The cost of a small bottle of sanitizer is ₹10 and that of a large bottle is ₹15. In June, the company sold 1000 bottles and recorded a total sale of ₹12,750. Seeing the increased demand, the company decided to increase the price of both sanitizer bottles by ₹2 each. In the next month, the company sold 2500 bottles and recorded a total sale of ₹34,250. Based on the above information, answer the following questions: (i) Form a linear equation in two variables representing the sale for June. (1) (ii) Form a linear equation in two variables representing the sale for July. (1) (iii) (A) How many sanitizer bottles of each type were actually sold in June? (2) OR (iii) (B) How many sanitizer bottles of each type were sold in July? (2)

Show answer
Let x and y be the numbers of small and large bottles sold. (i) 10x + 15y = 12750 (or 2x + 3y = 2550). (ii) 12x + 17y = 34250. (iii)(A) x + y = 1000 and 10x + 15y = 12750. 10x + 15(1000 – x) = 12750 ⇒ 5x = 2250 ⇒ x = 450, y = 550. 450 small and 550 large bottles were sold in June. OR (iii)(B) x + y = 2500 and 12x + 17y = 34250. 12(2500 – y) + 17y = 34250 ⇒ 5y = 4250 ⇒ y = 850, x = 1650. 1650 small and 850 large bottles were sold in July.

CBSE 2026 board paper · 1 mark

The pair of equations x = 2 and y = 3 represent the lines which are

  1. intersecting at (–2, –3)
  2. intersecting at (2, 3)
  3. parallel
  4. coincident
Show answer
intersecting at (2, 3)

CBSE 2026 sample paper · 1 mark

If 2024x + 2025y = 1 ; 2025x + 2024y = -1, then x - y =

  1. 0
  2. – 2
  3. 2
  4. – 1
Show answer
– 2

CBSE 2026 board paper · 1 mark

Three lines k1, k2, k3 represent three different equations: line k1 : x + 2y = 3, line k2 : x + 2y = 6 and line k3 : px + qy = r. Solution of the equations represented by lines k1 and k3 is x = 3, y = 0, while solution of equations represented by lines k2 and k3 is x = 4, y = 1. Which of the following is the equation of line k3 ?

  1. x - y = 3
  2. x - y = -3
  3. x + y = 3
  4. x + y = 1
Show answer
x - y = 3