# How do you solve the simultaneous equations y - 3x = 2 and 3x + 2y = -14?

Jul 27, 2015

The solution for the system of equations is:
color(blue)(x=-2, y =-4

#### Explanation:

y−3x=2
y=color(blue)(2+3x ..............equation $\left(1\right)$

3x+2y=−14.....equation $\left(2\right)$

Solving by substitution
Substituting equation $1$ in equation $2$

3x+2y=−14

3x+2(color(blue)(2+3x))=−14

3x+4+6x=−14

9x=−14-4

$9 x = - 18$
color(blue)(x=-2

Substituting $x$ in equation $1$ to find $y$
$y = 2 + 3 x$
$y = 2 + 3 \left(- 2\right)$
$y = 2 - 6$
color(blue)(y=-4