# How do you solve the system of equations 8x + 5y = - 38 and - 6x + y = 38?

May 16, 2017

See a solution process below:

#### Explanation:

Step 1) Solve the second equation for y)

$- 6 x + y = 38$

$\textcolor{red}{6 x} - 6 x + y = \textcolor{red}{6 x} + 38$

$0 + y = 6 x + 38$

$y = 6 x + 38$

Step 2) Substitute $6 x + 38$ for $y$ in the first equation and solve for $x$:

$8 x + 5 y = - 38$ becomes:

$8 x + 5 \left(6 x + 38\right) = - 38$

$8 x + \left(5 \cdot 6 x\right) + \left(5 \cdot 38\right) = - 38$

$8 x + 30 x + 190 = - 38$

$\left(8 + 30\right) x + 190 = - 38$

$38 x + 190 = - 38$

$38 x + 190 - \textcolor{red}{190} = - 38 - \textcolor{red}{190}$

$38 x + 0 = - 228$

$38 x = - 228$

$\frac{38 x}{\textcolor{red}{38}} = - \frac{228}{\textcolor{red}{38}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{38}}} x}{\cancel{\textcolor{red}{38}}} = - 6$

$x = - 6$

Step 3) Substitute $- 6$ for $x$ in the solution to the second equation at the end of Step 1 and calculate $y$:

$y = 6 x + 38$ becomes:

$y = \left(6 \times - 6\right) + 38$

$y = - 36 + 38$

$y = 2$

The solution is: $x = - 6$ and $y = 2$ or $\left(- 6 , 2\right)$