Answer
The solution is $(0,-4)$.
Work Step by Step
The given system of equations is
$y=-2x-4$ ...... (1)
$y=2x-4$ ...... (2)
Add equation (1) and (2).
$\Rightarrow y+y=-2x-4+2x-4$
Add like terms.
$\Rightarrow 2y=-8$
Divide each side by $2$.
$\Rightarrow \frac{2y}{2}=\frac{-8}{2}$
Simplify.
$\Rightarrow y=-4$
Substitute $-4$ for $y$ in equation (2).
$\Rightarrow -4=2x-4$
Add $4$ to each side.
$\Rightarrow -4+4=2x-4+4$
Simplify.
$\Rightarrow 0=2x$
Divide each side by $2$.
$\Rightarrow \frac{0}{2}=\frac{2x}{2}$
Simplify.
$\Rightarrow 0=x$
Check $(x,y)=(0,-4)$
Equation (1):
$\Rightarrow y=-2x-4$
$\Rightarrow -4=-2(0)-4$
$\Rightarrow -4=0-4$
$\Rightarrow -4=-4$
True.
Equation (2):
$\Rightarrow y=2x-4$
$\Rightarrow -4=2(0)-4$
$\Rightarrow -4=0-4$
$\Rightarrow -4=-4$
True.
Hence, the solution is $(0,-4)$.
