How do you solve #3y - 2x = 11# and #y + 2x = 9# using substitution?

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Answer 1 · 2018-03-10T04:44:17

#y=5 and #x=2#

#2x + y =9#
#-2x + 3y =11#

We need to solve #2x + y = 9# for #y#

#2x + y = 9#
#y=9 -2x#

Now substitute #-2x + 9# for #y# in #-2x + 3y =11#

#-2x + 3y =11#

#-2x + 3(-2x+9)=11#

Distribute

#-2x + (3)(-2x)+(3)(9)=11#

#-2x - 6x + 27 = 11#

#-8x + 27 = 11#

#-8x = 11 - 27#

#-8x = -16#

#x=(-16)/(-8)#

#x=2#

Now substitute #2# for #x# in #y=-2x+9#

#y=-2x + 9#

#y=-2(2)+9#

#y=-4 + 9#

#y=5#

Thus,

The answers are #y=5# and #x=2#