How do you solve the system?: #2(x-4) + y=6, 3x-2(y-3)=13#

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Answer 1 · 2015-11-02T03:05:28

#x = 5, y = 4#

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Answer 2 · 2015-11-02T03:06:31

First expand the system and then use simultaneous equations to get #x=5# and #y=4#

Expanding and simplifying the system

#2(x-4) + y =2x-8+y=6#

Therefore,
#2x+y=14# #(1)#

#3x -2(y-3) =3x-2y+6=13#

Therefore,
#3x-2y=7# #(2)#

Simultaneous Equations

#(#2 #times# #(1)##)# #+# #(2)#

#4x+2y+28# #(1)#
#3x -2y=7# #(2)#

Cancel out the #y# terms and equate:

#7x=35#
#x=5#

Sub #x# back into #(1)#:

#2(5)+y=14#
#y=4#