Answer
The solution is $(1,6)$.
Work Step by Step
The given system of equations is
$x+2y=13$ ...... (1)
$-x+y=5$ ...... (2)
Add equation (1) and (2).
$\Rightarrow x+2y-x+y=13+5$
Add like terms.
$\Rightarrow 3y=18$
Divide each side by $3$.
$\Rightarrow \frac{3y}{3}=\frac{18}{3}$
Simplify.
$\Rightarrow y=6$
Substitute $6$ for $y$ equation (1).
$\Rightarrow x+2(6)=13$
Simplify.
$\Rightarrow x+12=13$
Subtract $12$ from each side.
$\Rightarrow x+12-12=13-12$
Simplify.
$\Rightarrow x=1$
Check $(x,y)=(1,6)$
Equation (1):
$\Rightarrow x+2y=13$
$\Rightarrow 1+2(6)=13$
$\Rightarrow 1+12=13$
$\Rightarrow 13=13$
True.
Equation (2):
$\Rightarrow -x+y=5$
$\Rightarrow -1+6=5$
$\Rightarrow 5=5$
True.
Hence, the solution is $(1,6)$.
