How do you solve #x + 2y = 7# and #2x - 3y = -5#?

1 Answer
Jun 5, 2016

Answer:

You could solve using substitution.

Explanation:

#x + 2y = 7#
#2x -3y = -5#

We can take one of these equations and solve for one variable, and plug that into the variable in the other equation. Let's use the first equation.

#x + 2y = 7# (We are solving for x)
#x = 7 - 2y# (We now have #x#, so we can plug this into #x# in the other equation)

#2x - 3y =-5#
#2(7 - 2y) - 3y =-5# (Plug in #7 - 2x# from the other equation)
#14 - 4y -3y = -5# (Distribute)
#-7y = -19#
#y = 19/7# (We have the solution for #y#, time to find #x#)

#x + 2(19/7) = 7# (Plug in #y#)
#x + 38/7 = 7#
#x = 11/7# (We have the x value)

The solutions are: #x = 11/7#, and #y = 19/7#.