How do you solve the following system?: #-6x -3y =1, -2x +4y = -5#

1 Answer
Andrew I.
Feb 7, 2016

#x =11/30,y = -16/15#

Explanation:

We have the equations:
#-6x-3y=1# and
#-2x+4y=-5#

I would say the best way to procede is to eliminate the #x# terms. Multiply the 2nd equation by 3 so that the coefficient of #x# on the 2nd equation is the same as the coefficient of #x# on the first equation giving:

That means the 2nd equation becomes:

#-6x+12y=-15#

Now subtract the equations from each other to eliminate the #x# terms and get:

#(-6x-3y)-(-6x+12y) = 1 - (-15) #
#-> -15y = 16 -> y = -16/15#

Now put this value of #y# back into either of the original equations to find #x#, we'll choose the first equation:

#-6x -3(-16/15) = 1#
#-6x +16/5 = 1#
#-> -6x = 1-16/5=-11/5#
Thus:
#x =11/30#

Hence our final solution. It is good practice to put these values into the other equation to check that they work.

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