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

1 Answer
Mar 10, 2018

Answer:

#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.