# How do you solve the following system: 5x + 8y = -2, 6x+2y=-4?

Aug 31, 2017

See a solution process below:

#### Explanation:

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

$6 x + 2 y = - 4$

$- \textcolor{red}{6 x} + 6 x + 2 y = - \textcolor{red}{6 x} - 4$

$0 + 2 y = - 6 x - 4$

$2 y = - 6 x - 4$

$\frac{2 y}{\textcolor{red}{2}} = \frac{- 6 x - 4}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} y}{\cancel{\textcolor{red}{2}}} = \frac{- 6 x}{\textcolor{red}{2}} - \frac{4}{\textcolor{red}{2}}$

$y = - 3 x - 2$

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

$5 x + 8 y = - 2$ becomes:

$5 x + 8 \left(- 3 x - 2\right) = - 2$

$5 x + \left(8 \cdot - 3 x\right) - \left(8 \cdot 2\right) = - 2$

$5 x - 24 x - 16 = - 2$

$\left(5 - 24\right) x - 16 = - 2$

$- 19 x - 16 = - 2$

$- 19 x - 16 + \textcolor{red}{16} = - 2 + \textcolor{red}{16}$

$- 19 x - 0 = 14$

$- 19 x = 14$

$\frac{- 19 x}{\textcolor{red}{- 19}} = \frac{14}{\textcolor{red}{- 19}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 19}}} x}{\cancel{\textcolor{red}{- 19}}} = - \frac{14}{19}$

$x = - \frac{14}{19}$

Step 3) Substitute $- \frac{14}{19}$ for $x$ in the solution to the second equation at the end of Step 1 and calculate $y$:

$y = - 3 x - 2$ becomes:

$y = \left(- 3 \times - \frac{14}{19}\right) - 2$

$y = \frac{42}{19} - 2$

$y = \frac{42}{19} - \left(\frac{19}{19} \cdot 2\right)$

$y = \frac{42}{19} - \frac{38}{19}$

$y = \frac{4}{19}$

The Solution Is: $x = - \frac{14}{19}$ and $y = \frac{4}{19}$ or $\left(- \frac{14}{19} , \frac{4}{19}\right)$