Answer
$x=-2$ and $y=3$
$\{ (-2,3) \}$
Work Step by Step
The given system is
$2x=11-5y$ ... (1)
Isolate all variables
$2x+5y=11$ ... (2)
and $3x-2y=-12$ ... (3) .
Multiply equation (2) by $3$ and equation (3) by $-2$.
$6x+15y=33$ ... (4)
$-6x+4y=+24$ ... (5)
Add equation (4) and (5).
$6x+15y-6x+4y=33+24$
$19y=57$
Divide both sides by $19$.
$\frac{19y}{19}=\frac{57}{19}$
Simplify.
$y=3$.
Plug $y=3$ into equation (1).
$2x=11-5(3)$
$2x=11-15$
$2x=-4$
Divide both sides by $2$
$\frac{2x}{2}=-\frac{4}{2}$
$x=-2$.
