How do you solve the system of equations #3x + 3y = 9# and #5x - 3y = 7#?

1 Answer
Nov 6, 2016

#y = 1#, #x = 2#

Explanation:

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

#3x + 3y = 9#

#(3x + 3y)/3 = 9/3#

#(3x)/3 + (3y)/3 = 9/3#

#x + y = 3#

#x + y - y = 3 - y#

#x = 3 - y#

Step 2) Substitute #3 - y# for #x# in the second equation:

#5x - 3y = 7#

#5(3 - y) - 3y = 7#

#15 - 5y - 3y = 7#

#15 - 8y = 7#

#15 - 8y + 8y - 7 = 7 + 8y - 7#

#15 - 7 = 8y#

#8 = 8y#

#8/8 = (8y)/8#

#y = 1#

Step 3) Substitute #1# for #y# in the solution from Step 1.

#x = 3 - y#

#x = 3 - 1#

#x = 2#