Introduction to Linear Inequalities

System of Linear Inequalities

Review of Graphing Linear Inequalities

• Change to Slope-Intercept Form if needed (Get y by itself).

• Plot y intercept and use the slope to find the second point.

• Determine if dashed or solid line (< , > is dashed and < , > is solid).

• Determine whether to shade above or below ( > shade above, < shade below).

Multiple Choice

Review: Which inequality matches the graph shown?

• y < x - 2

• y > 2x - 1

• y > x - 2

• y > x - 2

System of Inequalities

Is made up of 2 or more linear inequalities.

Solution to a System of Inequalities

Is all ordered pairs that make ALL inequalites true.

**WHERE THE SHADED PORTIONS OF THE BOTH INEQUALITIES OVERLAP.**

Steps to Graphing Systems of Inequalities

• Make sure both inequalities are in Slope-Intercept Form.

• Graph both inequalities (Don't forget to determine dashed or solid line and shade above or shade below).

• Heavily shade in the portion where the shaded regions overlap. This is the solution to the system of inequalities.

• At this point, downsize this screen and go watch the video that is also attached on Google Classroom and then come back here for the practice problems.

Practice #1

Graph the following system of inequalities.

y > -3x + 5

y < x - 2

Answer Practice #1

Practice #2

Solve the following system of inequalities.

y < 2

x > -1

Answer Practice #2