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

Jul 9, 2018

$x = - 2 , y = 4$

#### Explanation:

Plugging the second equation

$y = - 3 x - 2$ in the first one:

$- 3 x - 2 x - 2 = 8$
adding $2$ on both sides and collexting like Terms

$- 5 x = 10$

$x = - 2$ so $y = 6 - 2 = 4$

Jul 9, 2018

$\left(x , y\right) \to \left(- 2 , 4\right)$

#### Explanation:

$- 2 x + y = 8 \to \left(1\right)$

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

$\text{equation "(2)" expresses y in terms of } x$

$\text{substitute "y=-3x-2" into equation } \left(1\right)$

$- 2 x - 3 x - 2 = 8$

$- 5 x - 2 = 8$

$\text{add 2 to both sides}$

$- 5 x = 8 + 2 = 10$

$\text{divide both sides by } - 5$

$x = \frac{10}{- 5} \Rightarrow x = - 2$

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

$y = 6 - 2 = 4$

$\text{the point of intersection } = \left(- 2 , 4\right)$
graph{(y+3x+2)(y-2x-8)=0 [-10, 10, -5, 5]}