Question

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

Answer 1

Label the equations with numbers:
`2x+y=5` (1)
`y=3x+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=`3/5`=0.6

Now, we have to find y.
We can substitute x=`3/5` into y =3x+2(2) to find y.
y=3x`3/5`+2=`19/5`=3.8

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