How do you solve the following system?: #3x +2y =8 , 6x +9y = -3#

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Answer 1 · 2015-12-01T00:04:37

#x = 26/5# and #y = -19/5#

We multiply the first equation by #2# to get the same coefficient for #x# in both equations. The system then becomes

#6x + 4y = 16#

#6x + 9y = -3#

Subtract the first equation from the second:

#6x + 9y = -3#

#- (6y + 4y = 16)#

In other words we add vertically:

#6x + 9y = -3#

#- 6y - 4y = -16#

The result is

#0 + 5y = -19#

So #5y = -19# and dividing both sides by #5# we get #y = -19/5#.
We substitute this value of y into the first equation:

#3x - 38/5 = 8#

Therefore #3x = 8 + 38/5# (subtracting #2y = -38/5# from each side),
So

#3x = (40 + 38)/5 = 78/5# and #x = 26/5#