Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables MCQs with answers

Answer: (b) exactly one solution

a₁/a₂ = 3/4 and b₁/b₂ = 5/(−2) = −5/2. Since 3/4 ≠ −5/2, the lines intersect, so there is exactly one solution.

Answer: (d) parallel

a₁/a₂ = 6/4 = 3/2, b₁/b₂ = (−9)/(−6) = 3/2, c₁/c₂ = 4/5. So a₁/a₂ = b₁/b₂ ≠ c₁/c₂: the lines are parallel.

Answer: (c) consistent, with infinitely many solutions

a₁/a₂ = 5/15 = 1/3, b₁/b₂ = 2/6 = 1/3, c₁/c₂ = (−9)/(−27) = 1/3. All three are equal, so the lines coincide: infinitely many solutions, and the pair is consistent (dependent).

Answer: (b) 6x − 8y + 12 = 0

6x − 8y + 12 = 0 is 2(3x − 4y + 6) = 0: a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2. Option (a) and option (d) have the x and y ratios equal but a different constant ratio (parallel); (c) has 3/4 ≠ −4/−3 (intersecting).

Answer: (c) 2

Two lines either meet in one point, never meet, or coincide. So a pair has one solution, none, or infinitely many; exactly two is impossible.

Answer: (c) (4, −1)

x = 4 is a vertical line and y = −1 a horizontal one; they always meet, at the point (4, −1).

Answer: (d) 3

3x − 4(7 − 2x) = 5 gives 3x − 28 + 8x = 5, so 11x = 33 and x = 3 (then y = 1).

Answer: (a) 3

The y-coefficients are 3 and −3, opposite in sign, so adding removes y: 9x = 27, x = 3.

Answer: (d) (0, 0) and (2, 3)

c = 0, so x = 0 and y = 0 give the same point (0, 0) twice. Another value is needed: x = 2 gives 6 − 2y = 0, y = 3, so (2, 3). (3, 2) gives 9 − 4 = 5 ≠ 0.

Answer: (c) 33°

The acute angles of a right triangle are complementary: x + y = 90 and x − y = 24, so 2y = 66, y = 33°.