How do you solve the following linear system #3x-2y=8, 2x-3y=-6 #?

1 Answer
Jun 9, 2016

Answer:

#(x,y)=color(green)(""(7.2,6.8))#

Explanation:

Given
[1]#color(white)("XXX")3x-2y=8#
[2]#color(white)("XXX")2x-3y=-6#

Multiplying [1] by #3# and [2] by #2#
[3]#=#[1]#xx3color(white)("XXX")9x-6y=color(white)("XX")24#
[4]#=#[2]#xx2color(white)("XXX")underline(4x-6y=-12)#

Subtracting [4] from [5]
[6]#=#[5]#-#[4]#color(white)("XXX")5x=36#

Dividing both sides by #5#
[7]#=#[6]#div5color(white)("XXX")x=7.2#

Substituting #7.2# for #x# in [1]
[8]#color(white)("XXXXXX")3(7.2)-2y=8#
Simplifying
[9]#color(white)("XXXXXX")21.6-2y=8#

[10]#color(white)("XXXXXX")2y=13.6#

[11]#color(white)("XXXXXX")y=6.8#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For verification purposes substitute #(x,y)=(7.2,6.8)# into [2]
#color(white)("XXXXXXX")2x-3y#

#color(white)("XXXXXXXXXX")=2(7.2)-3(6.8)#

#color(white)("XXXXXXXXXX")=14.2-20.4#

#color(white)("XXXXXXXXXX")=-6color(white)("XXX")#as given.