How do you solve the system #2x+2y=7# and #x-2y=-1# using substitution?

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Answer 1 · 2016-11-09T23:03:24

#y = 3/2# and #x = 2#

Step 1) Solve the second equation for #x# while keeping the equation balanced:

#x - 2y + 2y = -1 + 2y#

#x = 2y - 1#

Step 2) Substitute #2y - 1# for #x# in the first equation and solve for #y# while keeping the equation balanced.

#2(2y - 1) + 2y = 7#

#4y - 2 + 2y = 7#

#6y - 2 = 7#

#6y - 2 + 2 = 7 + 2#

#6y = 9#

#(6y)/6 = 9/6#

#y = 3/2#

Step 3) Substitute #3/2# for #y# in the second equation and solve for #x# while keeping the equation balanced:

#x = 2(3/2) - 1#

#x = 3 - 1#

#x = 2#