How do you solve the following system: #3x - 2y = 9, 2x + 3y = 34#?

1 Answer
Alan P.
Jan 16, 2016

#(x,y)= (95/13, 84/13)#

Explanation:

Given:
[1]#color(white)("XXX")3x-2y=9#
[2]#color(white)("XXX")2x+3y=34#

Multiply [1] by 3 and [2] by 2 to get equivalent coefficients for #y#
[3]#color(white)("XXX")9x-6y=27#
[4]#color(white)("XXX")6x+6y=68#

Add [3] and [4]
[5]#color(white)("XXX")13x= 95#

Divide both sides by 13
[6]#color(white)("XXX")x=95/13#

Substitute #13# for #x# in [1]
[7]#color(white)("XXX")3*(95/13)-2y=9#

Simplify
[8]#color(white)("XXX")2y= 285/13-9 = (285-117)/13 = 168/13#

[9]#color(white)("XXX")y=84/13#

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