# How do you solve the system 2x - y = 2 and -x + 5y = 3?

$2 x - y = 2 \implies 2 x - 2 = y$
$- x + 5 y = 3 \implies - x + 5 \cdot \left(2 x - 2\right) = 3$
$- x + 10 x - 10 = 3 \implies 9 x - 10 = 3 \implies 9 x = 13 \implies x = \frac{9}{13}$
$y = 2 x - 2 \implies y = 2 \cdot \left(\frac{9}{13}\right) - 2 = \left(\frac{18}{13}\right) - 2$
$= \left(\frac{18}{13}\right) - \left(\frac{26}{13}\right) = \frac{8}{13}$