# How do you solve 2x + y = 5 and y = 3x + 2 using substitution?

Apr 7, 2015

Label the equations with numbers:
$2 x + y = 5$ (1)
$y = 3 x + 2$ (2)

As we can see in both equations, the similar variable is $y$.

We can get rid of the value $y$ by substituting equation (2) into (1).
Here, we can see that y=3x+2(2) and that we can place y=3x+2 (2) into the y variable in (1)
2x+ y =5 (1)
y =3x+2(2)

After substituting (2) into (1), we get:
2x+(3x+2)=5

Simplify the equation...
5x+2=5

Now, we can find x
5x=5-2
5x=3
x=$\frac{3}{5}$=0.6

Now, we have to find y.
We can substitute x=$\frac{3}{5}$ into y =3x+2(2) to find y.
y=3x$\frac{3}{5}$+2=$\frac{19}{5}$=3.8

Hence, y=3.8 and x=0.6 (0.6,3.8)