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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