# How do solve the following linear system?:  1/3x + 3y = 9 , 8x + 3y= -9 ?

Dec 26, 2015

You can solve it either using substitution or elimination, but the following proof will use substitution.

#### Explanation:

$\frac{1}{3} x$ + 3y = 9
3y = 9 - $\frac{1}{3} x$
y = 3 - $\frac{1}{9} x$
8x + 3(3 - $\frac{1}{9} x$) = -9
8x + 9 - $\frac{1}{3} x$ = -9
$\frac{23}{3} x$ + 9 = -9
$\frac{23}{3} x$ = -18
23 = -54x
$- \frac{54}{23}$ = x
8($- \frac{54}{23}$) + 3y = -9
$- \frac{432}{23}$ + 3y = -9
$- \frac{432}{23}$ + 9 = -3y
$- \frac{225}{23}$ = -3y
$\frac{75}{23}$ = y

The solution set is ($- \frac{54}{23}$, $\frac{75}{23}$)