# How do you solve the following system?: -2x -8y =3, 3x -2y = -3

Jun 1, 2016

To substitute, we need to solve for one of the variables and then substitute this into the other equation.

#### Explanation:

$- 2 x = 3 + 8 y$

$x = - \frac{3}{2} - 4 y$

$\therefore 3 \left(- \frac{3}{2} - 4 y\right) - 2 y = - 3$

$- \frac{9}{2} - 12 y - 2 y = - 3$

$- 14 y = - 3 + \frac{9}{2}$

$- 14 y = \frac{3}{2}$

$y = \frac{\frac{3}{2}}{-} 14$

$y = - \frac{3}{28}$

Solving for x:

$3 x - 2 \left(- \frac{3}{28}\right) = - 3$

$3 x + \frac{6}{28} = - 3$

$3 x = - 3 - \frac{3}{14}$

$3 x = - \frac{42}{14} - \frac{3}{14}$

$3 x = - \frac{45}{14}$

$x = - \frac{45}{42}$

$x = - \frac{15}{14}$

Therefore, the solution set is $\left\{- \frac{15}{14} , - \frac{3}{28}\right\}$. Don't forget solutions always have to be presented in the form $\left\{x , y\right\}$.

Hopefully this helps!