How do you solve the following system?: #-1/2x+5y=-20 , 3x-2y=1 #

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Answer 1 · 2016-07-12T14:42:27

#x=-105/42# and #y=-119/28#

The given system
#-1/2x+5y=-20# and #3x-2y=1#

Let us use the method of substitution

From the second equation #3x-2y=1#

#x=(1+2y)/3#

We use the second in the first equation

#-1/2x+5y=-20#

#-1/2((1+2y)/3)+5y=-20#

#-((1+2y)/3)+10y=-40#

#((1+2y)/3)-10y=40#

#1+2y-30y=120#

#-28y=119#

#y=-119/28#
~~~~~~~~~~~~~~~~~~~~~~~

Solve for #x#

#x=(1+2(-119/28))/3#

#x=(28-238)/84#

#x=-210/84#

#x=-105/42#
~~~~~~~~~~~~~~~~~~~~~~

Checking:at #x=-105/42# and #y=-119/28#

#-1/2x+5y=-20#
#-1/2(-105/42)+5(-119/28)=-20#

#105/84-595/28=-20#

#(105-1785)/84=-20#

#(-1680)/84=-20#

#-20=-20

Also

#3x-2y=1#

#3(-105/42)-2(-119/28)=1#

#-105/14+119/14=1#

#14/14=1#

#1=1#

Correct ! at #x=-105/42# and #y=-119/28#

God bless....I hope the explanation is useful.