# How do you solve the system of equations: y=x+3 and 2x+2y=14?

Aug 14, 2015

The solutions for the system of equations is
color(blue)(x=2,y=5

#### Explanation:

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

$2 x + 2 y = 14$.....equation $\left(2\right)$

We can solve through substitution , by substituting equation $\left(1\right)$ in $\left(2\right)$ to find $x$:

$2 x + 2 \left(\textcolor{b l u e}{x + 3}\right) = 14$
$2 x + 2 x = 14 - 6$
$4 x = 8$
color(blue)(x=2

Now, we substitute $x$ in equation $1$ to find $y$
$y = x + 3$
$y = 2 + 3$
color(blue)(y=5