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

Nov 6, 2017

$y = - \frac{16}{23}$

$x = \frac{50}{23}$

#### Explanation:

$- x - 6 y = 2$
$4 x + y = 8$

Make $y$ the subject in the second equation:

$y = 8 - 4 x$

Then inject that as $y$ in the first equation:

$- x - 6 \left(8 - 4 x\right) = 2$

Expand and solve for $x$

$- x - 48 + 24 x = 2 \to 23 x = 50$

$x = \frac{50}{23}$

Place that $x$ value into the rearranged equation to find $y$

$y = 8 - \frac{200}{23}$

$y = \frac{184}{23} - \frac{200}{23}$

$y = - \frac{16}{23}$