Question

The linear equation 2x + 5y = 16 has
(a) a unique solution
(b) two solutions
(c) no solution
(d) infinitely many solutions

Answer 1

(d) infinitely many solutions
The linear equation is $2x+5y=16$ or, $y=\frac{16-2x}{5}$
When $x=3$, then $y=\frac{10}{5}=2$

When $x=8$, then $y=\frac{0}{5}=0$

When $x=13$, then $y=\frac{-10}{5}=-2$
Plotting these points $(3,2),(8,0)$ and $(13,-2)$ on the graph paper, we see that the equation has infinite solutions.