# How do you solve the following system: -29=5y-3x, 5x+2y=12 ?

Mar 22, 2018

$x = \frac{118}{31}$ and $y = - \frac{109}{31}$

#### Explanation:

We can eliminate a variable by subtracting out an equation.

For example, let's take 3 times the second plus five times the first:

$3 \left(5 x + 2 y = 12\right) \implies 15 x + 6 y = 36$
$5 \left(- 3 x + 5 y = - 29\right) \implies - 15 x + 25 y = - 145$
$31 y = - 109 \implies y = \frac{- 109}{31}$
We can now plug this into our second equation from before and get $x$:
$5 x + 2 \left(\frac{- 109}{31}\right) = 12 \implies 5 x = 12 + \frac{218}{31} = \frac{590}{31}$
$x = \frac{118}{31}$