How do you solve the following system?: # -9x - 3y = 2 , 3x – y = -1 #

1 Answer
Dec 23, 2016

Answer:

#color(green)(x=-5/18, y= 1/6)#

Explanation:

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

Multiplying [2] by #3#
#color(white)("XXXX")3xx(3x-y)=3xx(-1)#
[3]#color(white)("XXX")9x-3y=-3#

Adding [1] and [3]
#color(white)("XXXX")-9x-3y=2#
#color(white)("XXXXX")underline(9x-3y)=underline(-3)#
[4]#color(white)("XXXXXX")-6y=-1#

Dividing [4] by #(-6)#
#color(white)("XXX")(cancel(-6)y)/cancel(-6)=(cancel(-)1)/(cancel(-)6)#
[5]#color(white)("XXX")y=1/6#

Substituting #(1/6)# for #y# in [2]
[6]#color(white)("XXX")3x-(1/6)=-1#

Adding #1/6# to both sides of [6]
#color(white)("XXX")3xcancel(-(1/6))cancel(+1/6)=-1+1/6#

[7]#color(white)("XXX")3x=-5/6#

Dividing both sides of [7] by #3#
#color(white)("XXX")(cancel(3)x)/cancel(3)= -(5/6)/3#

[8]#color(white)("XXX")x=-5/18#