# How do you solve the following system: 3x + 8y = -2, x +4y = 16?

Mar 14, 2016

x = -34
$y = \frac{25}{2}$

#### Explanation:

x + 4y = 16 --> x = 16 - 4y
Substitute x by (16 - 4y) into the second equation -->
3x + 8y = -2
3(16 - 4y) + 8y = - 2
48 - 12y + 8y = -2
-4y = - 2 - 48 = -50
$y = - \frac{50}{-} 4 = \frac{25}{2}$ --> $x = 16 - 4 \left(\frac{25}{2}\right) = - 34$
Check
$3 x + 8 y = 3 \left(- 34\right) + 8 \left(\frac{25}{2}\right) = - 102 + 100 = - 2$. OK