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

##### 1 Answer

Graphically the two equations are just different representations of the same graph, and they, therefore, do not have one definite answer.

#### Explanation:

Normally you would treat the two equations as functions and draw a graph of each. Where they intersect you will find your solution since the solution has to fulfill both equations at the same time.

Here, though, you will find that the two lines overlap.

Both are linear functions, and if you set

Similarly

The two equations, therefore are just two different representations of the same line:

graph{2x-3y=21 [-22.8, 22.8, -11.4, 11.42]}

Algebraically we can see it this way:

Take

We see that the second equation is converted to the first one, so they are identical and, therefore, represent the same equation.