# How do you solve the following linear system: 3x + 2y = –5 , x-2y=13 ?

##### 1 Answer
May 21, 2018

See a solution process below:

#### Explanation:

Step 1) Solve the second equation for $x$:

$x - 2 y = 13$

$x - 2 y + \textcolor{red}{2 y} = 13 + \textcolor{red}{2 y}$

$x - 0 = 13 + 2 y$

$x = 13 + 2 y$

Step 2) Substitute $\left(13 + 2 y\right)$ for $x$ in the first equation and solve for $y$:

$3 x + 2 y = - 5$ becomes:

$3 \left(13 + 2 y\right) + 2 y = - 5$

$\left(3 \cdot 13\right) + \left(3 \cdot 2 y\right) + 2 y = - 5$

$39 + 6 y + 2 y = - 5$

$39 + \left(6 + 2\right) y = - 5$

$39 + 8 y = - 5$

$39 - \textcolor{red}{39} + 8 y = - 5 - \textcolor{red}{39}$

$0 + 8 y = - 44$

$8 y = - 44$

$\frac{8 y}{\textcolor{red}{8}} = - \frac{44}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} y}{\cancel{\textcolor{red}{8}}} = - \frac{4 \times 11}{\textcolor{red}{4 \times 2}}$

$y = - \frac{11}{2}$

Step 3) Substitute $- \frac{11}{2}$ for $y$ in the solution to the second equation at the end of Step 1 and calculate $x$:

$x = 13 + 2 y$ becomes:

$x = 13 + \left(2 \times - \frac{11}{2}\right)$

$x = 13 + \left(- 11\right)$

$x = 2$

The Solution Is:

$x = 2$ and $y = - \frac{11}{2}$

Or

$\left(2 , - \frac{11}{2}\right)$