Question

How do you solve this system of equations: `0.5x + y = 4.5 , y = x + 3`?

Answer 1

`x=1`
`y=4`

Explanation:

To solve this system of equations, you need to use the substitution method because only one of the variables is defined.

First, substitute for y
`0.5x+(x+3)=4.5`

Then, combine like terms (Ignore the parentheses)
`1.5x+3=4.5`

Finally, solve for x
`1.5x+3=4.5`
`x=1`

Since you now know what x is, substitute it in the other equation
`y=1+3`
`y=4`

Now that you know what both of the variables are, substitute for all the variables to check your answer
`0.5(1)+4=4.5` (correct)
`4=1+3` (correct)

Since both of the variables work, we can now come to a conclusion about our answer
`x=1`
`y=4`

We can write our answer like this
`(1,4)`