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

Mar 3, 2018

$x = 1$
$y = 4$

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
$0.5 x + \left(x + 3\right) = 4.5$

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

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

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
$0.5 \left(1\right) + 4 = 4.5$ (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
$\left(1 , 4\right)$