Question

How do you solve `2x+2y=14` and `2x-y=5` using substitution?

Answer 1

`x = 4, y = 3`

Explanation:

First you want to find a definition for either `x` or `y` in terms of the other, using the second equation.

`2x - y = 5`
`2x = y + 5`
`y = 2x - 5`

Now you can substitute this into the first equation.

`2x + 2y = 14`
`2x + 2(2x - 5) = 14`
`6x - 10 = 14`
`6x = 24`
`x = 4`

With this value, substitute into anything and it should give you `y`. Lets use the direct equation for `y` we found.

`y = 2x - 5`
`y = 2 * 4 - 5`
`y = 3`

You can substitute these values into any of the equations and they should work, if they are correct.