# How do you solve 3y = 14 + x and x + 22 = 5y?

Sep 9, 2015

The solution for the system of equations is
color(blue)(x=-2, y=4

#### Explanation:

$3 y = 14 + x$....equation $\left(1\right)$

$x + 22 = 5 y$
x=color(blue)( 5y-22......equation $\left(2\right)$

We can solve using the method of substitution.
Substituting equation $2$ in equation $1$:

$3 y = 14 + x$

3y = 14 +color(blue)( 5y-22

$3 y = - 8 + 5 y$
$8 = 5 y - 3 y$

$2 y = 8$
color(blue)(y=4

Now we find $x$ by substituting $y$ in equation 2:
$x = 5 y - 22$

$x = 5 \cdot 4 - 22$

$x = 20 - 22$

color(blue)(x=-2