How do you solve the following system?: # 1/4x-3/7y=1 , 3/2x - 8y = 2 #

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Answer 1 · 2016-05-14T12:07:03

#x = 24/19# and #y = 14/19#

Given the system:

#1/4x - 3/7y = 1#

#3/2x - 8y = 2#

Multiply the first equation by #4# to get:

#x - 12/7y = 4#

Add #12/7y# to both sides to get:

#x = 12/7y+4#

Substitute this expression for #x# in the second equation to get:

#2 = 3/2(12/7y+4)-8y#

#=18/7y+6-8y#

#=(18-56)/7y+6#

#=-38/7y+6#

Add #38/7y-2# to both ends to get:

#38/7y = 4#

Multiply both sides by #7/38# to get:

#y = 14/19#

Then we find:

#x = 12/7y+4 = 12/7(14/19)+4 = 24/19#