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

##### 1 Answer

Feb 25, 2016

#### Answer:

There is no single solution to the system of equations.

#### Explanation:

Given

[1]

[2]

Suppose we attempt this one "by substitution"

Substitute

[3]

Simplifying

[4]

[5]

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.