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.