# How do you solve the following system: 6x + y = 2, 2x + 3y = 34?

Mar 25, 2018

$x = - \frac{7}{4}$
$y = \frac{25}{2}$

#### Explanation:

Solve using substitution:
$6 x + y = 2$
$2 x + 3 y = 34$

The first equation when solved for $y$:
$y = - 6 x + 2$

Substitute for $y$ into the second equation:
$2 x + 3 \left(- 6 x + 2\right) = 34$

Distribute:
$2 x - 18 x + 6 = 34$

Combine like terms:
$- 16 x + 6 = 34$

Solve for x:
$- 16 x = 28$
$x = \frac{28}{-} 16$
$x = - \frac{7}{4}$

Solve for y by plugging in for $x$:
$y = - 6 \left(- \frac{7}{4}\right) + 2$
$y = \frac{42}{4} + 2$
$y = \frac{21}{2} + \frac{4}{2}$
$y = \frac{25}{2}$