# How do you solve the following system?:  3x+3y= -7 , 3x − y = 30

Feb 1, 2017

$y = - 9 \frac{1}{4} , x = 6 \frac{11}{12}$

#### Explanation:

$3 x + 3 y = - 7 - - - - - - - 1$

$3 x - y = 30 - - - - - - - - 2$

$4 y = - 37$----------------------------------$1 - 2$

$y = - \frac{37}{4}$

$y = - 9 \frac{1}{4}$

substitute $y = - \frac{37}{4}$ in-------2

$3 x - \left(- \frac{37}{4}\right) = 30$

$3 x + \frac{37}{4} = 30$

$3 x = 30 - \frac{37}{4}$

$3 x = \frac{120}{4} - \frac{37}{4}$

$3 x = \frac{83}{4}$

multiply both sides by 4

$12 x = 83$

$x = \frac{83}{12}$

$x = 6 \frac{11}{12}$

substitute $y = - \frac{37}{4} , x = \frac{83}{12}$ in-------2

$3 \left(\frac{83}{12}\right) - \left(- \frac{37}{4}\right) = 30$

$\frac{249}{12} + \frac{37}{4} = \frac{30}{1}$

$\frac{249 + 111 = 360}{12}$

$\frac{249}{12} + \frac{111}{12} = \frac{360}{12}$

$\frac{360}{12} = \frac{360}{12}$