# How do you solve 4x - y = -8 and x + 3y = -17?

Jul 8, 2017

See a solution process below:

#### Explanation:

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

$x + 3 y = - 17$

$x + 3 y - \textcolor{red}{3 y} = - 17 - \textcolor{red}{3 y}$

$x + 0 = - 17 - 3 y$

$x = - 17 - 3 y$

Step 2) Substitute $\left(- 17 - 3 y\right)$ for $x$ in the first equation and solve for $y$:

$4 x - y = - 8$ becomes:

$4 \left(- 17 - 3 y\right) - y = - 8$

$\left(4 \times - 17\right) - \left(4 \times 3 y\right) - y = - 8$

$- 68 - 12 y - 1 y = - 8$

$- 68 + \left(- 12 - 1\right) y = - 8$

$- 68 + \left(- 13\right) y = - 8$

$- 68 - 13 y = - 8$

$\textcolor{red}{68} - 68 - 13 y = \textcolor{red}{68} - 8$

$0 - 13 y = 60$

$- 13 y = 60$

$\frac{- 13 y}{\textcolor{red}{- 13}} = \frac{60}{\textcolor{red}{- 13}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 13}}} y}{\cancel{\textcolor{red}{- 13}}} = - \frac{60}{13}$

$y = - \frac{60}{13}$

Step 3) Substitute $- \frac{60}{13}$ for $y$ in the solution to the second equation at the end of Step 1 and calculate $y$:

$x = - 17 - 3 y$ becomes:

$x = - 17 - \left(3 \cdot - \frac{60}{13}\right)$

$x = - 17 - \left(- \frac{180}{13}\right)$

$x = - 17 + \frac{180}{13}$

$x = \left(\frac{13}{13} \cdot - 17\right) + \frac{180}{13}$

$x = - \frac{221}{13} + \frac{180}{13}$

$x = - \frac{41}{13}$

The solution is: $x = - \frac{41}{13}$ and $y = - \frac{60}{13}$ or $\left(- \frac{41}{13} , - \frac{60}{13}\right)$