Answer
$(-2,0)$
Work Step by Step
The given system of equations is
$\Rightarrow x+y=-2$ ...... (1)
$\Rightarrow -3x+y=6$ ...... (2)
Solve for $y$ in equation (2).
$\Rightarrow y=6+3x$ ...... (3)
Substitute $6+3x$ for $y$ in equation (1).
$\Rightarrow x+6+3x=-2$
Add like terms.
$\Rightarrow 6+4x=-2$
Subtract $6$ from each side.
$\Rightarrow 6+4x-6=-2-6$
Simplify.
$\Rightarrow 4x=-8$
Divide each side by $4$.
$\Rightarrow \frac{4x}{4}=\frac{-8}{4}$
Simplify.
$\Rightarrow x=-2$
Substitute $-2$ for $x$ in equation (3).
$\Rightarrow y=6+3(-2)$
Simplify.
$\Rightarrow y=6-6$
$\Rightarrow y=0$
Check
Equation (1)
$\Rightarrow x+y=-2$
$\Rightarrow -2+0=-2$
$\Rightarrow -2=-2$
True.
Check
Equation (2)
$\Rightarrow -3(-2)+0=6$
$\Rightarrow -6+0=6$
$\Rightarrow -6=-6$
True.
Hence, the solution is $(-2,0)$.
