GATE 2023 MN – Question 41
Three straight-line equations have (slope, intercept) pairs (2, 3), (4, 5), and (6, 2). Classify the simultaneous system.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (D) No solution
Explanation
The first two lines satisfy 2x+3 = 4x+5 at x=−1, y=1. The third line gives y=6(−1)+2=−4 at that x. Thus no point lies on all three lines, D. Distinct slopes guarantee pairwise intersections but do not guarantee one common intersection.