# How do you solve the simultaneous equations 2x+3y=6  and 3x-2y=22?

Jul 23, 2015

$\left\{\begin{matrix}x = 6 \\ y = - 2\end{matrix}\right.$

#### Explanation:

Simply multiply the first equation thoroughly by $2$ and the second equation by $3$ and subtract the results...

After the described multiplication, we get the result as

$4 x + 6 y = 12$
$9 x - 6 y = 66$
stackrel("---------------------------")

$13 x = 78 \implies x = \frac{78}{13} = 6$

Putting the value of $y$ into the first equation, we have

$2 \cdot 6 + 3 y = 6$

$3 y = 6 - 12$

$3 y = - 6 \implies x = \frac{\left(- 6\right)}{3} = - 2$