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

1 Answer
Mar 10, 2018

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.