Question

How do you solve the system `x - 2y = 2` and `x + y = 5`?

Answer 1

`x = 4, y = 1`

Explanation:

The quickest way in this particular set is probably by substitution.

Rearranging the first equation,
`x = 2y + 2`

Substituting into the second equation,
`2y + 2 + y = 5`

Collecting terms and rearranging
`3y = 5-2`

That is
`3y = 3`
which implies
`y = 1`

Substituting this value for `y` into the first equation
`x - 2 = 2`
which implies
`x = 4`

It is always worth checking the solution, so substituting these values into the second equation gives
`4 + 1 = 5` for the left hand side of the equation, which is equal to the right hand side of the equation, as expected.