Answer
$(-5,1) $ is not a solution of the system.
Work Step by Step
A solution of a system of two equations in two variables is an ordered pair of numbers that makes both equations true.
Substituting $x=-5, y=1$ into each equation,
$ x+5y=0$
$ (-5)+5(1)\stackrel{?}{=}0$
$-5+5=0,\qquad $...the first equation is true for $(-5,1)$
$y=2x+9$
$1\stackrel{?}{=}2(-5)+9$
$1\neq-10+9\qquad $...the second equation is not true for $(-5,1)$
$(-5,1) $ is not a solution of the system.