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

1 Answer
Isabella
Apr 7, 2018

x = -16, y = 11

Explanation:

I’m going to be using elimination:

First isolate 4 by subtracting 3x from both sides:

#3x + 4 = -4y#
#-3x -4y =4#

Now I’m going to line the two equations up to see which variable I can cancel out first

#x+2y=6#
#-3x-4y=4#

I choose #y# because it seems to be the cleanest out of the two. Now multiply the first equation by 2 in order to cancel out #y# and then solve for #x#

#2(x+2y=6) = 2x+4y=12 #

#2x+4y=12#
#+#
#-3x-4y=4#
———————
#-x=16#
#x=-16#

Time to solve for #y# by plugging in #-16# for #x# in either equation. It’s best to choose the equation that seems more efficient

#(-16) +2y=6#
#+16#

#{2y}/2 =22/2#

#y=11#

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