Answer
One common solution $\Rightarrow$ $(4,-1)$
Work Step by Step
We use the addition method below:
We add the two equations:
$2x-5y=13$
$5x+7y=13$
Multiply the first equation by $5$ and the second equation by $-2$ to cancel $x$:
$+10x-25y=+65$
$\underline{-10x-14y=-26}$
$-39y=39$
Solve for $y$:
$y=\frac{39}{-39}=-1$
Substitute into any of the two equations and solve for $x$:
$2x-5y=13$
$2x-5(-1)=13$
$2x+5=13$
$2x=13-5$
$2x=8$
$x=\frac{8}{2}$
$x=4$
