How do solve the following linear system?: # 9 x-6y =3 , x + y= 12 #?

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Answer 1 · 2017-01-17T09:17:30

#x=5# and #y=7#

#9x-6y=3#
#x+y=12#

Using the second equation, determine a value for #y#.

#x+y=12#

Subtract #x# from both sides.

#y=12-x#

Reduce the first equation by dividing all terms by #3#.

#9x-6y=3#

#3x-2y=1#

Substitute #y# with #color(red)((12-x))#.

#3x-2color(red)((12-x))=1#

Open the brackets and simplify. The product of two negatives is a positive.

#3x-24+2x=1#

#5x-24=1#

Add #24# to both sides.

#5x=25#

Divide both sides by #5#.

#x=5#

In the second equation, substitute #x# with #color(blue)5#.

#x+y=12#

#color(blue)5+y=12#

Subtract #5# from each side.

#y=7#