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

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Answer 1 · 2015-05-24T09:25:30

Noticing the same term in #y# in both equations, we can eliminate #y# quickly as follows:

Subtract the first equation from the second to get:

#x = (3x+y)-(2x+y) = 11 - (-9) = 20#

Substitute this value of #x# into the first equation to get:

#-9 = (2xx20)+y = 40+y#

Subtract #40# from both sides to get:

#y = -9 -40 = -49#

As a quick check, substitute these values for #x# and #y# into the left hand side of the second equation:

#3x+y = (3xx20)+(-49) =60-49 = 11#