Answer
The solution is $(2,-3)$.
Work Step by Step
The given system of equations is
$\Rightarrow 2y+x=-4$ ...... (1)
$\Rightarrow y-x=-5$ ...... (2)
Add $x$ to each side of equation (2).
$\Rightarrow y-x+x=-5+x$
$\Rightarrow y=x-5$ ...... (2)
Substitute $x-5$ for $y$ in equation (1).
$\Rightarrow 2(x-5)+x=-4$
Use distributive property.
$\Rightarrow 2x-10+x=-4$
Add like terms.
$\Rightarrow 3x-10=-4$
Add $10$ to each side.
$\Rightarrow 3x-10+10=-4+10$
Simplify.
$\Rightarrow 3x=6$
Divide each side by $3$.
$\Rightarrow \frac{3x}{3}=\frac{6}{3}$
Simplify.
$\Rightarrow x=2$
Substitute $2$ for $x$ in equation (2).
$\Rightarrow y-2=-5$
Add $2$ to each side.
$\Rightarrow y-2+2=-5+2$
Simplify.
$\Rightarrow y=-3$
Check: $(x,y)=(2,-3)$
Equation (1)
$\Rightarrow 2y+x=-4$
$\Rightarrow 2(-3)+2=-4$
$\Rightarrow -6+2=-4$
$\Rightarrow -4=-4$
True.
Equation (2)
$\Rightarrow y-x=-5$
$\Rightarrow -3-2=-5$
$\Rightarrow -5=-5$
True.
Hence, the solution is $(2,-3)$.
