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

Jul 3, 2017

$x = 9 , y = 3$

Explanation:

We have: $x + y = 12$ and $x - y = 6$

First, let's solve both equations for $y$:

$R i g h t a r r o w x + y = 12$

$R i g h t a r r o w y = 12 - x$

$\mathmr{and}$

$R i g h t a r r o w x - y = 6$

$R i g h t a r r o w y = x - 6$

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

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 $y = 3$.