How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent x+y=12 and xy=6?

1 Answer
Jul 3, 2017

x=9,y=3

Explanation:

We have: x+y=12 and xy=6

First, let's solve both equations for y:

x+y=12

y=12x

and

xy=6

y=x6

Then, let's graph both of these rearranged equations:

enter image source here
Image from Desmos

As you can see from the graph, the system is consistent because there is a point of intersection, i.e. a solution to the system of equations.

The solutions to the system of equations are x=9 and y=3.