How do solve the following linear system?: # -9x + 6y = -2 , 3x-y=7 #?

1 Answer
Alan P.
Mar 20, 2017

#(x,y)=(40/9,19/3)#

Explanation:

Given
[1]#color(white)("XXX")-9x+6y=-2#
[2]#color(white)("XXX")3x-y=7#

Multiplying [2] by #3#
[3]#color(white)("XXX")9x-3y=21#

Adding [1] and [3]
[4]#color(white)("XXX")3y=19#

Dividing [4] by #3#
[5]#color(white)("XXX")y=19/3#

Substituting #19/4# for #y# in [2]
[6]#color(white)("XXX")3x-19/3=7#

Adding #19/4# to both sides of [6] and simplifying the right side
[7]#color(white)("XXX")3x=40/3#

Dividing [7] by #3#
[8]#color(white)("XXX")x=40/9#

You might want to simplify this as #(x,y)=(3 4/9,6 1/3)#
however
leaving these values in their improper fraction forms will probably make the verification easier (...and you always do this; right?)

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