How do you solve #2x – 2y = 2#, #y = 3x – 17# using substitution?

1 Answer
Mar 15, 2016

Answer:

This is very simple to do since a variable is already isolated, which is what is necessary to solve a system by substitution.

Explanation:

#2x - 2y = 2 -> y = 3x - 17#

#2x - 2(3x - 17) = 2#

#2x - 6x + 34 = 2#

#-4x = -32#

#x = 8#

Now, substituting 8 for x, we get:

#y = 3(8) - 17#

#y = 24 - 17#

#y = 7#

Thus, the solution set is #{8, 7}#. Remember: solution sets must always be presented in the form #{x, y}#!

Practice exercises:

  1. Solve the following by substitution. Leave answers in fractional form when necessary.

a) #x + 2y = -4, 2x - 5y = 6#

b) #2x + 7y = 11, -6x + 3y = 14#

Good luck!