Answer
If we get the result $0=0$, then there was at least one side that was multiplied by a non-zero constant.
Work Step by Step
Example:
$y=-2x+5$
$4x+2y=10$
$y=-2x+5$
$y+2x=-2x+5+2x$
$y+2x=5$
If we double this equation ($y+2x=5$), then we get $2y+4x=10$. This equation is the same as $4x+2y=10$. Since these equations are the same, then we know that at least one side was multiplied by a non-zero constant.