# How do you solve the following system:  -6x + 5y = 4 , x-10y=10 ?

Jan 10, 2016

$x = - \frac{18}{11}$, $y = - \frac{64}{55}$

#### Explanation:

To solve by elimination you will need to make coefficients of x or y "match" so that when you add or subtract the equations one of the variables will be eliminated.

If we double the first equation we get:

$- 12 x + 10 y = 8$

$x - 10 y = 10$

Now if we add the two new equations, we will eliminate y and will be able to solve an equation in x.

$- 11 x = 18 \implies x = - \frac{18}{11}$

Substitute this back into one of the original equations to find y.

$- 6 \cdot - \frac{18}{11} + 5 y = 4$
$\frac{108}{11} + 5 y = 4$
$5 y = - \frac{64}{11}$
$y = - \frac{64}{55}$