UPPSC 2025

Q. The linear equation 3x – 5y = 15 has

a) a unique solution
b) no solution
c) two solutions
d) infinitely many solutions
Correct Answer: d) infinitely many solutions

Question from UPPSC Prelims CSAT 2025

Explanation:

3x – 5y = 15 is a single linear equation in two variables, representing a straight line in the xy-plane.

A line has infinitely many points, hence infinitely many solutions over the real numbers. Equivalently, letting x = t (any real), we get y = (3t − 15)/5, yielding infinitely many (x, y) pairs. A unique solution would require another independent equation; none is given.

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