# How do you solve the system x=-4y and 3x+2y=20?

Nov 25, 2015

You may substitute $- 4 y$ for every $x$ in the second equation

#### Explanation:

$3 \cdot \left(- 4 y\right) + 2 y = 20 \to - 12 y + 2 y = 20$
$- 10 y = 20 \to y = - 2$

Now reverse the substitution to find $x$
$x = - 4 y = - 4 \cdot \left(- 2\right) = 8$

Just to make sure, you can plug these values in the 2nd:
$3 x + 2 y = 3 \cdot 8 + 2 \cdot \left(- 2\right) = 24 - 4 = 20$ Check!