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

Mar 10, 2018

$x = 4 , y = 1$

#### Explanation:

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

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

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

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

That is
$3 y = 3$
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.