# How do you solve x - 9y = -80 and 2y - 2x = 16 using substitution?

May 27, 2018

$\left(x , y\right) \to \left(1 , 9\right)$

#### Explanation:

$x - 9 y = - 80 \to \left(1\right)$

$2 y - 2 x = 16 \to \left(2\right)$

$\text{rearrange equation "(1)" expressing x in terms of y}$

$x = - 80 + 9 y \to \left(3\right)$

$\textcolor{b l u e}{\text{substitute "x=-80+9y" in equation }} \left(2\right)$

$2 y - 2 \left(- 80 + 9 y\right) = 16$

$2 y + 160 - 18 y = 16$

$- 16 y + 160 = 16$

$\text{subtract 160 from both sides}$

$- 16 y = 16 - 160 = - 144$

$\text{divide both sides by } - 16$

$y = \frac{- 144}{- 16} = 9$

$\text{substitute "y=9" in equation } \left(3\right)$

$x = - 80 + 81 = 1$

$\text{solution is } \left(x , y\right) \to \left(1 , 9\right)$
graph{(y-1/9x-80/9)(y-x-8)=0 [-20, 20, -10, 10]}