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