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Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables Assertion-reason questions with answers

2 assertion-reason questions on Pair of Linear Equations in Two Variables, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): The pair 2x + 5y − 1 = 0 and 4x + 10y − 3 = 0 has no solution. Reason (R): If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines are parallel and the pair has no solution.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

a₁/a₂ = b₁/b₂ = 1/2 and c₁/c₂ = 1/3. A is true, and it is true precisely because of the condition in R.

Question 2
Assertion (A): The lines x = 3 and y = −2 meet in exactly one point. Reason (R): For this pair, a₁/a₂ ≠ b₁/b₂.
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Answer: (c) A is true, but R is false.

A is true: a vertical and a horizontal line meet at (3, −2). R is false: written as 1·x + 0·y − 3 = 0 and 0·x + 1·y + 2 = 0, a₁/a₂ = 1/0 is undefined, not 'unequal'; the answer comes from the geometry.

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