How do you solve the system of equations #2x+2y=9# and #2x-y=3#?

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Answer 1 · 2017-01-02T04:09:15

#x=2 1/2# and #y=2#

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

From the second equation, we derive a value for #2x#.

#2x-y=3#

Add #y# to each side.

#2x=y+3#

In the first equation, substitute #2x# with #color(red)((y+3))#.

#2x+2y=9#

#color(red)((y+3))+2y=9#

Open the brackets and simplify.

#y+3+2y=9#

#3y+3=9#

Subtract #3# from each side.

#3y=6#

Divide both sides by #3#.

#y=2#

In the second equation, substitute #y# with #color(blue)(2)#.

#2x-y=3#

#2x-2=3#

Add #2# to each side.

#2x=5#

Divide both sides by #2#.

#x=5/2=2 1/2#