# How do you solve the following linear system 2x+3y= 3, 3x+y=3 ?

Feb 10, 2016

The easiest way in this situation would be substitution, and so I'll solve it that way for you.

#### Explanation:

To do substitution, you must isolate a variable.

$3 x + y = 3$

$y = 3 - 3 x$

$2 x + 3 \left(3 - 3 x\right) = 3$

$2 x + 9 - 9 x = 3$

$- 7 x = - 6$

$x = \frac{6}{7}$

Plugging in $\frac{6}{7}$ for x.

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

$y = 3 - \frac{18}{7}$

$y = \frac{3}{7}$

The solution set is $\left\{\frac{6}{7} , \frac{3}{7}\right\}$

Hopefully this helps!