# How do you solve the system 3x - 2y = 8 and 2x + 5y = -1?

Jun 25, 2017

$x = 2 , y = - 1$

#### Explanation:

This is a clear simultaneous equation.

$3 x - 2 y = 8$
$2 x + 5 y = - 1$

In order to solve this, either the x's or the y's must be balanced. It does not matter which one you start with.

For this, I'll balance the y's:

$15 x - 10 y = 40$ Every value is multiplied by 5.
$4 x + 10 y = - 2$ Every value is multiplied by 2.

Both y values can now be eliminated.

$15 x - 10 y + 4 x + 10 y = 19 x$
$40 - 2 = 38$

$19 x = 38$

Now solve for x.

$x = \frac{38}{19} = 2$

Put the value for x back into either equation to find y.

$3 x - 2 y = 8$
$3 \left(2\right) - 2 y = 8$
$6 - 2 y = 8$
$- 2 y = 8 - 6 = 2$

Rearrange to find y.

$- 2 y = 2$

Divide both sides by -2.

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

$y = - 1$