# How do you solve the system -3(5+x)=y and 5(x-3)=2y+4?

Jun 9, 2015

The solution for the system of equations is:
 color(blue)( x = -1 , y =-12

#### Explanation:

$- 3 \left(5 + x\right) = y$
$- 15 - 3 x = y$
$y + 3 x = - 15$ ............equation $\left(1\right)$

$5 x - 15 = 2 y + 4$
$5 x - 2 y = 4 + 15$
$5 x - \textcolor{b l u e}{2 y} = 19$................equation $\left(2\right)$

• Multiplying equation $\left(1\right)$ by $2$
$y + 3 x = - 15$
$\textcolor{b l u e}{2 y} + 6 x = - 30$ ...........equation $\left(3\right)$
• Adding equations $2 \mathmr{and} 3$ to eliminate $\textcolor{b l u e}{2 y}$

$5 x - \cancel{\textcolor{b l u e}{2 y}} = 19$
$\cancel{\textcolor{b l u e}{2 y}} + 6 x = - 30$
$11 x = - 11$
 color(blue)(x = -1

Substituting $x$ in equation $\left(1\right)$ to find $y$:
$y = - 15 - 3 x$
$y = - 15 - 3. \left(- 1\right)$
color(blue)(y = -12