# How do you solve the following system?: 3x +2y =8 , 6x +9y = -3

Dec 1, 2015

$x = \frac{26}{5}$ and $y = - \frac{19}{5}$

#### Explanation:

We multiply the first equation by $2$ to get the same coefficient for $x$ in both equations. The system then becomes

$6 x + 4 y = 16$

$6 x + 9 y = - 3$

Subtract the first equation from the second:

$6 x + 9 y = - 3$

$- \left(6 y + 4 y = 16\right)$

In other words we add vertically:

$6 x + 9 y = - 3$

$- 6 y - 4 y = - 16$

The result is

$0 + 5 y = - 19$

So $5 y = - 19$ and dividing both sides by $5$ we get $y = - \frac{19}{5}$.
We substitute this value of y into the first equation:

$3 x - \frac{38}{5} = 8$

Therefore $3 x = 8 + \frac{38}{5}$ (subtracting $2 y = - \frac{38}{5}$ from each side),
So

$3 x = \frac{40 + 38}{5} = \frac{78}{5}$ and $x = \frac{26}{5}$