Answer
The solution is $(-22,-26)$.
Work Step by Step
The given system of equations is
$\Rightarrow y=x-4$ ...... (1)
$\Rightarrow -2x+y=18$ ...... (2)
Substitute $x-4$ for $y$ in equation (2).
$\Rightarrow -2x+x-4=18$
Add like terms.
$\Rightarrow -x-4=18$
Add $x-18$ to each side.
$\Rightarrow -x-4+x-18=18+x-18$
Simplify.
$\Rightarrow -22=x$
Substitute $-22$ for $x$ in equation (1).
$\Rightarrow y=-22-4$
Simplify.
$\Rightarrow y=-26$
Check: $(x,y)=(-22,-26)$
Equation (1)
$\Rightarrow y=x-4$
$\Rightarrow -26=-22-4$
$\Rightarrow -26=-26$
True.
Equation (2)
$\Rightarrow -2x+y=18$
$\Rightarrow -2(-22)-26=18$
$\Rightarrow 44-26=18$
$\Rightarrow 18=18$
True.
Hence, the solution is $(-22,-26)$.
