# How do you solve the following system: 6x+2y=-4, x-5y=-9?

Jun 22, 2018

See a solution process below:

#### Explanation:

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

$x - 5 y = - 9$

$x - 5 y + \textcolor{red}{5 y} = - 9 + \textcolor{red}{5 y}$

$x - 0 = - 9 + 5 y$

$x = - 9 + 5 y$

Step 2) Substitute $\left(- 9 + 5 y\right)$ for $x$ in the first equation and solve for $y$:

$6 x + 2 y = - 4$ becomes:

$6 \left(- 9 + 5 y\right) + 2 y = - 4$

$\left(6 \times - 9\right) + \left(6 \times 5 y\right) + 2 y = - 4$

$- 54 + 30 y + 2 y = - 4$

$- 54 + \left(30 + 2\right) y = - 4$

$- 54 + 32 y = - 4$

$- 54 + \textcolor{red}{54} + 32 y = - 4 + \textcolor{red}{54}$

$0 + 32 y = 50$

$32 y = 50$

$\frac{32 y}{\textcolor{red}{32}} = \frac{50}{\textcolor{red}{32}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{32}}} y}{\cancel{\textcolor{red}{32}}} = \frac{25}{16}$

$y = \frac{25}{16}$

Step 3) Substitute $\frac{25}{16}$ for $y$ in the solution to the second equation at the end of Step 1 and calculate $x$:

$x = - 9 + 5 y$ becomes:

$x = - 9 + \left(5 \times \frac{25}{16}\right)$

$x = \left(\frac{16}{16} \times - 9\right) + \frac{125}{16}$

$x = - \frac{144}{16} + \frac{125}{16}$

$x = - \frac{19}{16}$

The Solution Is:

$x = - \frac{19}{16}$ and $y = \frac{25}{16}$

Or

$\left(- \frac{19}{16} , \frac{25}{16}\right)$