How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #y = 2/3x# and #y = - 1/3 x + 6#?

1 Answer
Alan P.
Apr 20, 2016

#(x,y)=(-6,-4)#
This is a consistent system of equations (since it has a single solution)

Explanation:

Given:
#color(white)("XXX")y=2/3x#
#color(white)("XXX")y=-1/3x+6#

Multiplying everything in both equations by #3#
#color(white)("XXX")3y=2x#
#color(white)("XXX")3y=-x+18#

Subtracting the second from the first:
#color(white)("XXX")0=3x+18#
#color(white)("XXX")rArr x=-6#

and since #3y=2x#
#color(white)("XXX")3y=-12#
#color(white)("XXX")rArr y=-4#

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