# How do you solve the following system of equations?: 2x + 15y = -4 , -3x + 3y=10?

##### 1 Answer
Jan 7, 2016

$x = - \frac{54}{17}$ and $y = \frac{8}{51}$

#### Explanation:

$2 x + 15 y = - 4$$\ldots \ldots \ldots \ldots \ldots . . \left(i\right)$
$- 3 x + 3 y = 10$$\ldots \ldots \ldots \ldots \ldots \left(i i\right)$

Multiply $\left(i\right)$ by $3$ and $\left(i i\right)$ by $2$

$\implies 6 x + 45 y = - 12$
$\mathmr{and} - 6 x + 6 y = 20$

By addition we have

$51 y = 8$

$\implies y = \frac{8}{51}$

Put $y = \frac{8}{51}$ in $\left(i\right)$

$\implies 2 x + 15 \left(\frac{8}{51}\right) = - 4$

$\implies 102 x + 120 = - 204$

$\implies 102 x = - 324$

$\implies x = - \frac{54}{17}$