Question

The linear equation 3x − 5y = has
(a) a unique solution
(b) two solutions
(c) infinitely many solutions
(d) no solution

Answer 1

(c) infinitely many solutions
Given linear equation: $3x-5y=15$
Or, $x=\frac{5y+15}{3}$

When $y=0$, $x=\frac{15}{3}=5$.

When $y=3$, $x=\frac{30}{3}=10$.

When $y=-3$, $x=\frac{0}{3}=0$.

Thus, we have the following table:

$\text{x}$	5	10	0
$y$	0	3	-3

Plot the points $A(5,0),B(10,3)$ and $C(0,-3)$. Join the points and extend them in both the directions.
We get infinite points that satisfy the given equation.
Hence, the linear equation has infinitely many solutions.