# A.2.21.2 Solutions and Not Solutions

- Author:
- Katie Akesson

In the opener we saw that (0, 5) and (-5, 10) are not solutions to the inequality 2x + 3y __<__ 12, but (6, 0) and (-1, -1) are solutions.
On the coordinate plane below, there **A LOT** more points that are both solutions and not solutions to the inequality 2x + 3y __<__ 12. Each point that is a solution is marked with a blue dot and each point that is not a solution is marked with an yellow x.
The equation 2x + 3y = 12 is also graphed on the coordinate grid below.
What do you notice about the plotted points?

Your goal for this activity is to find the region that contains solutions to the inequality x + y > 10.
To do this complete the following steps on the graph below:
a) graph the line x + y = 10
b) find 3 points that **are not** solutions to the inequality and graph them
c) find 3 points that **are **solutions to the inequality and graph them
d) decide if the the points (5, 5) and (-2, 12) **are or are not** solutions to the inequality x + y > 10
Then, describe the region that contains solutions to the inequality x + y > 10.

How can we tell where exactly the solution region stops and non-solution region starts?

The inequalities x > y and x __>__ y are each graphed in one of the graphs below.
Match each inequality with its graph.