How do you solve the following linear system #x+y= -3, 3x+y=3 #?

1 Answer
Shwetank Mauria
Sep 4, 2016

#x=3# and #y=-6#

Explanation:

There are many methods for solving pair of linear equations in two variables. Prominent among them is substitution method.

First equation #x+y=-3# gives us #x=-y-3#. Putting this in second equation we get

#3×(-y-3)+y=3# or

#-3y-9+y=3# or

#-2y=3+9=12# i.e. #y=-6# and #x=-(-6)-3=6-3=3#

Another method could be multiplying first equation by #3# which gives us #3x+3y=-9#. Now subtracting second equation #3x+y=3# from this, we get #2y=-12# or #y=-6#. Putting this in first we get #x-6=-3# i.e. #x=3#.

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