How do you solve the system of equations #x+ 2y = - 4# and #2y - x = - 8#?

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Answer 1 · 2017-06-21T03:38:35

#x=2#, #y=-3#

Here we have a system of two linear equations.

#x+2y =-4# [A]

#2y-x=-8 -> -x+2y =-8# [B]

[A] + [B] #-> 4y =-12#

#y=-12/4 = -3#

Replacing for #y# in [A]

#x+2xx(-3) =-4#

#x=-4+6 = +2#

Check result in [B]

#2xx(-3)-2 = -6-2 = -8#

Results are correct.

Answer 2 · 2017-06-21T03:55:16

#(2,-3)#

#x+2y=-4#
#2y-x=-8#

We can use the elimination method to isolate a variable. In this case, we'll start off with isolating #y#.

Add the two equations together.

#x+2y=-4#
#-x +2y=-8#

#4y=-12#

You can now solve this new equation for #y#.

#y=-3#

Plug the value for #y# back into one of the original equations.

#x+2(-3)=-4#
#x-6=-4#

#x=2#

Your solution is #(2,-3)#.