# How do you solve the following system?: 3x+3y=-21 , 4x-3y=15

Jun 4, 2016

$x = - \frac{6}{7} , y = - \frac{129}{12}$

#### Explanation:

use the addition/elimination method to solve for x.

$3 x + 3 y = - 21$
$4 x - 3 y = 15$

3x + 4x = 7x, 3y - 3y = 0 and -21 + 15 = -6

$\therefore 7 x = - 6$ so $x = - \frac{6}{7}$

sub in and test

$3 \left(- \frac{6}{7}\right) + 3 y = - 21$
$- \frac{18}{7} + 3 y = - 21$

multiply everything by 7 to eliminate the fraction

$- 18 + 21 y = - 147$

$21 y = - 129$

$y = - \frac{129}{12}$

.

$4 \left(- \frac{6}{7}\right) - 3 y = 15$
$- \frac{24}{7} - 3 y = 15$

multiply everything by 7 to eliminate the fraction

$- 24 - 21 y = 105$

$- 21 y = 129$

$y = - \frac{129}{12}$