How do you solve x + 4y = 19 and y = -2x - 4?

May 18, 2018

Answer:

$\left(x , y\right) \to \left(- 5 , 6\right)$

Explanation:

$x + 4 y = 19 \to \left(1\right)$

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

$\text{substitute "y=-2x-4" into equation } \left(1\right)$

$x + 4 \left(- 2 x - 4\right) = 19 \leftarrow \textcolor{b l u e}{\text{distribute}}$

$\Rightarrow x - 8 x - 16 = 19$

$\Rightarrow - 7 x - 16 = 19$

$\text{add 16 to both sides}$

$\Rightarrow - 7 x = 19 + 16 = 35$

$\text{divide both sides by } - 7$

$\Rightarrow x = \frac{35}{- 7} = - 5$

$\text{substitute "x=-5" into equation } \left(2\right)$

$\Rightarrow y = \left(- 2 \times - 5\right) - 4 = 10 - 4 = 6$

$\text{the point of intersection of the 2 equations } = \left(- 5 , 6\right)$
graph{(y+1/4x-19/4)(y+2x+4)=0 [-20, 20, -10, 10]}