# How do you solve the following system?:  -9x - 3y = 2 , -7/2x - 1/2y = -3

Mar 24, 2018

$x = - 2 / 3 , y = 4 / 3$

#### Explanation:

Simplifying first equation,

$- 9 x - 3 y = 2$

Dividing by 3 on both sides,

$\Rightarrow - 3 x - y = 2 / 3 \ldots \ldots \ldots \ldots . \left(1\right)$

Now for second equation,

$- 7 x / 2 - y / 2 = - 3$

Multiplying both sides by 2,

$\Rightarrow - 7 x - y = - 6 \ldots \ldots \ldots \ldots . \left(2\right)$

Now adding (1) and (2), we get:

$\left(- 3 x - y\right) + \left(- 7 x - y\right) = 2 / 3 + \left(- 6\right)$

$\Rightarrow - 10 x = - 20 / 3$

$\Rightarrow x = - 2 / 3$

Now, put $x = - 2 / 3$ in (1),

$- 3 \cdot \left(- 2 / 3\right) - y = 2 / 3$

$\Rightarrow y = 4 / 3$

$\therefore x = - 2 / 3 , y = 4 / 3$