# How do you solve the following system?: 2x +y = 6 , x + 3y = -8

Feb 27, 2017

See the entire solution process below:

#### Explanation:

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

$x + 3 y = - 8$

$x + 3 y - \textcolor{red}{3 y} = - 8 - \textcolor{red}{3 y}$

$x + 0 = - 8 - 3 y$

$x = - 8 - 3 y$

Step 2) Substitute $- 8 - 3 y$ for $x$ in the first equation and solve for $y$:

$2 x + y = 6$ becomes:

$2 \left(- 8 - 3 y\right) + y = 6$

$- 16 - 6 y + y = 6$

$- 16 - 5 y = 6$

$\textcolor{red}{16} - 16 - 5 y = \textcolor{red}{16} + 6$

$0 - 5 y = 22$

$- 5 y = 22$

$\frac{- 5 y}{\textcolor{red}{- 5}} = \frac{22}{\textcolor{red}{- 5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} y}{\cancel{\textcolor{red}{- 5}}} = - \frac{22}{5}$

$y = - \frac{22}{5}$

Step 3) Substitute $- \frac{22}{5}$ for $y$ in the solution to the second equation at the end of Step 1 and calculate $x$:

$x = - 8 - 3 y$ becomes:

$x = - 8 - \left(3 \times - \frac{22}{5}\right)$

$x = - 8 - \left(- \frac{66}{5}\right)$

$x = - 8 + \frac{66}{5}$

$x = \left(\frac{5}{5} \times - 8\right) + \frac{66}{5}$

$x = - \frac{40}{5} + \frac{66}{5}$

$x = \frac{26}{5}$

The solution is: $x = \frac{26}{5}$ and $y = - \frac{22}{5}$ or $\left(\frac{26}{5} , - \frac{22}{5}\right)$