How do you solve the system y = 2/3x - 7 and 2x - 3y = 21?

1 Answer
Alan P.
Feb 25, 2016

There is no single solution to the system of equations.

Explanation:

Given
[1]#color(white)("XXX")y=2/3x-7#
[2]#color(white)("XXX")2x-3y=21#

Suppose we attempt this one "by substitution"
Substitute #2/3x-7# (from equation [1]) for #y# in equation [2]
[3]#color(white)("XXX")2x-3(2/3x-7)=21#

Simplifying
[4]#color(white)("XXX")2x-2x+21=21#
[5]#color(white)("XXX")21=21#
Whoa! we ended up with a true equation but no variable solution!

What does this mean?
It means that the original equations were not independent; they are just rearranged versions of each other.

In terms of a graph the two equations represent the same line and therefore do not intersect to give a single solution.

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