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

Jan 10, 2016

$x = - \frac{32}{7}$ $y = - \frac{12}{7}$

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 multiply the second equation by 4 we get:

$- 4 x + 6 y = 8$

$4 x - 20 y = 16$

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

$- 14 y = 24 \implies y = - \frac{12}{7}$

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

$x - 5 \cdot - \frac{12}{7} = 4$
$x + \frac{60}{7} = 4$
$x = 4 - \frac{60}{7} = - \frac{32}{7}$
$x = - \frac{32}{7}$