# How do you solve the system of equations x+ y = 8 and - 2x + 3y = 9?

Aug 6, 2018

$\left(x , y\right) \to \left(3 , 5\right)$

#### Explanation:

$\text{we can use the "color(blue)"substitution method}$

$x + y = 8 \to \left(1\right)$

$- 2 x + 3 y = 9 \to \left(2\right)$

$\text{from } \left(1\right) \to x = 8 - y \to \left(3\right)$

$\text{substitute "x=8-y" into equation } \left(2\right)$

$- 2 \left(8 - y\right) + 3 y = 9$

$- 16 + 2 y + 3 y = 9$

$\text{add 16 to both sides}$

$5 y = 9 + 16 = 25$

$\text{divide both sides by 5}$

$y = \frac{25}{5} = 5$

$\text{substitute "y=5" into equation } \left(3\right)$

$x = 8 - 5 = 3$

$\text{point of intersection is } \left(3 , 5\right)$
graph{(y+x-8)(y-2/3x-3)=0 [-10, 10, -5, 5]}