How do you solve the following system?: #-2x -2y =1, 2x -y = -2#

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Answer 1 · 2018-04-24T11:25:00

#x=-5/6#
#y=1/3#

Given -

#-2x-2y=1# -----------(1)
#2x-y=-2#--------------(2)

Solve equation (2) for #y#

#-y=-2-2x#

Multiply both sides by #-1#

#y=2+2x#

Substitute #y=2+2x# in equation (1)

#-2x-2(2+2x)=1#

#-2x-4-4x=1#

#-4-6x=1#

#-6x=1+4=5#

#x=-5/6#

Substitute #x=5/6#in equation (2)

#2(-5/6)-y=-2#

#-5/3-y=-2#

#-y=-2+5/3=(-6+5)/3=-1/3#

#-y= -1/3#

#y=1/3#