# How do you solve the system of equations 2x+3y=6 and 3x+3y=14?

Apr 1, 2015

$x = 8 , y = - \frac{10}{3}$

Our aim is finding a similarity in the two equations. In this problem, we already have it: $3 y$

So, lets rewrite the second equation:

2) $3 x + 3 y = 14$
$3 y = 14 - 3 x$

Now, we can replace $3 y$ with $14 - 3 x$ in the first equation.

$2 x + \left(14 - 3 x\right) = 6$
$2 x + 14 - 3 x = 6$
$- x = - 8$
$x = 8$

Now, we know the value of $x$. By using either first or second equation we can calculate the value of $y$. Lets use the second "2)" equation.

2) $3 x + 3 y = 14$
$3 \cdot 8 + 3 y = 14$
$24 + 3 y = 14$
$3 y = - 10$
$y = - \frac{10}{3}$