Answer
The solution is $(-2,2)$.
Work Step by Step
The given system of equations is
$-x+y=4$ ...... (1)
$x+3y=4$ ...... (2)
Add equation (1) and (2).
$\Rightarrow -x+y+x+3y=4+4$
Add like terms.
$\Rightarrow 4y=8$
Divide each side by $4$.
$\Rightarrow \frac{4y}{4}=\frac{8}{4}$
Simplify.
$\Rightarrow y=2$
Substitute $2$ for $y$ in equation (2).
$\Rightarrow x+3(2)=4$
Simplify.
$\Rightarrow x+6=4$
Subtract $6$ from each side.
$\Rightarrow x+6-6=4-6$
Simplify.
$\Rightarrow x=-2$
Check $(x,y)=(-2,2)$
Equation (1):
$\Rightarrow -x+y=4$
$\Rightarrow -(-2)+2=4$
$\Rightarrow 2+2=4$
$\Rightarrow 4=4$
True.
Equation (2):
$\Rightarrow x+3y=4$
$\Rightarrow -2+3(2)=4$
$\Rightarrow -2+6=4$
$\Rightarrow 4=4$
True.
Hence, the solution is $(-2,2)$.
