# Solutions to Linear Inequalities

- Author:
- Tim Brzezinski

- Topic:
- Coordinates, Inequalities

**A SOLUTION to a linear inequality of 2 variables is an ordered pair (**

*x*,*y*) whose coordinates satisfy the original inequality (i.e. make the original inequality true.)**For example, note the point (5, 3) shown in the applet below.**

**The graph of the inequality**

**is also shown.**

**(5, 3) is a SOLUTION**

**to the inequality**because ==> which is TRUE! Any point (

*x*,

*y*) that does NOT satisfy the original inequality (that is, does NOT make the original inequality true) is said NOT to be a solution to the given inequality. How many solutions (

*x*,

*y*) does the graph of an linear inequality of two variables have?

## 1.

Change the parameters *A*, *B*, and *C* by using the sliders or by inputting values in the input boxes. Drag the **yellow point** around in the graph of this linear inequality. Algebraically show that this point is a SOLUTION to this linear inequality.

## 2.

Pick a point (*x*, *y*) that does NOT lie in the graph of the **shaded blue region**. Show that this point is NOT a solution to this linear inequality.