How do solve the following linear system?: # 3/2x - 3y = -9/4 , 2/3x + 4y = -1 #?

1 Answer
Alan P.
Feb 19, 2016

#(x,y)=(-3/2,0)#

Explanation:

Given:
[1]#color(white)("XXX")3/2x-3y=-9/4#
[2]#color(white)("XXX")2/3x+4y=-1#
To make the solution easier we will clear the fractions by
multiplying [1] by #4# and [2] by #3# to get
[3]#color(white)("XXX")6x-12y=-9#
[4]#color(white)("XXX")2x+12y=-3#

Adding equations [3] and [4] gives
[5]#color(white)("XXX")8x=-12#
and after dividing by #8#
[6]#color(white)("XXX")x=-3/2#

Substituting #(-3/2)# (from [6]) for #x# in [2]
[7]#color(white)("XXX")2/3xx(-3/2)+4y=-1#
Simplifying
[8]#color(white)("XXX")y=0#

Graphically:
graph{(3/2x-3y+9/4)(2/3x+4y+1)=0 [-5.07, 2.725, -1.414, 2.483]}

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