# How do you solve this system of equations: y= - 6x - 13 and 7x + 2y = - 16 ?

Dec 14, 2017

$\left(x , y\right) \to \left(- 2 , - 1\right)$

#### Explanation:

$y = - 6 x - 13 \to \left(1\right)$

$7 x + 2 y = - 16 \to \left(2\right)$

$\textcolor{b l u e}{\text{Substitute "y=-6x-13" into equation }} \left(2\right)$

$\Rightarrow 7 x + 2 \left(- 6 x - 13\right) = - 16$

$\Rightarrow 7 x - 12 x - 26 = - 16$

$\Rightarrow - 5 x - 26 = - 16$

$\text{add 26 to both sides}$

$- 5 x \cancel{- 26} \cancel{+ 26} = - 16 + 26$

$\Rightarrow - 5 x = 10$

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

$\frac{\cancel{- 5} x}{\cancel{- 5}} = \frac{10}{- 5}$

$\Rightarrow x = - 2$

$\textcolor{b l u e}{\text{substitute "" this value into equation }} \left(1\right)$

$\Rightarrow y = \left(- 6 \times - 2\right) - 13 = 12 - 13 = - 1$

$\text{the point of intersection } = \left(- 2 , - 1\right)$
graph{(y+6x+13)(y+7/2x+8)((x+2)^2+(y+1)^2-0.04)=0 [-10, 10, -5, 5]}