How do solve the following linear system?: # 9 x-6y =3 , -3x -8y = -9 #?

1 Answer
Feb 3, 2016

Answer:

#(x,y) = (13/15,4/5)#

Explanation:

Given
[equation 1]#color(white)("XXX")9x-6y=3#
[equation 2]#color(white)("XXX")-3x-8y=-9#

If we multiply [equation 2] by #3# then the coefficient of #x# will be of the same magnitude as in [equation 1]
[equation 3]#color(white)("XXX")-9x-24y=-27#

Adding [equation 1] and [equation 3]
[equation 4]#color(white)("XXX")-30y=-24#

Dividing [equation 4] by #(-30)# gives
[equation 5]#color(white)("XXX")y= 24/30 = 4/5#

Substituting #4/5# for #y# in [equation 1]
[equation 6]#color(white)("XXX")9x-6xx4/5 =3#

[equation 7]#color(white)("XXX")9x=3+24/5=39/5#

Dividing [equation 7] by #9# gives
[equation 8]#color(white)("XXX")x=39/45=13/15#