# How do you solve the following linear system 2x-3y= 3, x+y=-3 ?

Dec 29, 2015

The solution for the system of equations is:
color(blue)(x=-6/5

color(blue)(y=-9/5

#### Explanation:

$\textcolor{b l u e}{2 x} - 3 y = 3$......equation $\left(1\right)$

$x + y = - 3$ , multiplying by $2$
$\textcolor{b l u e}{2 x} + 2 y = - 6$......equation $\left(2\right)$

Solving by elimination.

Subtracting equation $2$ from $1$

$\textcolor{b l u e}{2 x} - 3 y = 3$

$- \textcolor{b l u e}{2 x} - 2 y = + 6$

$- 5 y = 9$

color(blue)(y=-9/5

Finding $x$ from equation $2$:
$x + y = - 3$

$x = - 3 - y$

$x = - 3 - \left(- \frac{9}{5}\right)$
$x = - 3 + \frac{9}{5}$

$x = - \frac{15}{5} + \frac{9}{5}$

color(blue)(x=-6/5