# How do you solve the system of equations 3x - 2y = 13 and x = - y - 4?

May 5, 2017

$\left(1 , - 5\right)$

#### Explanation:

$3 \textcolor{red}{x} - 2 y = 13 \to \left(1\right)$

$\textcolor{red}{x} = - y - 4 \to \left(2\right)$

$\text{Since " (2)" is expressed with x as the subject, we can}$
$\text{substitute it directly into "(1)" and solve for y}$

$\Rightarrow 3 \left(- y - 4\right) - 2 y = 13$

$\Rightarrow - 3 y - 12 - 2 y = 13 \leftarrow \text{ distributing}$

$\Rightarrow - 5 y - 12 = 13 \leftarrow \text{ simplifying left side}$

$\text{add 12 to both sides}$

$- 5 y \cancel{- 12} \cancel{+ 12} = 13 + 12$

$\Rightarrow - 5 y = 25$

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

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

$\Rightarrow y = - 5$

$\text{substitute this value into "(2)" and evaluate for x}$

$y = - 5 \to x = - \left(- 5\right) - 4 = 5 - 4 = 1$

$\textcolor{b l u e}{\text{As a check}}$

Substitute these values for x and y into the left side of ( 1 ) and if equal to the right side then they are the solution.

$\text{left side } = \left(3 \times 1\right) - \left(2 \times - 5\right) = 3 + 10 = 13$

$\Rightarrow \text{point of intersection } = \left(1 , - 5\right)$
graph{(y+x+4)(y-3/2x+13/2)=0 [-10, 10, -5, 5]}