# 7.5 Systems of inequalities in two variables (Part 1)

#### 1 Introduction to liner inequalities.

Have the students explore inequalities on their own. The sources has sliders that will change different variables, which always students to visually see what changes on the graph when each variable is altered.

Play around with the sliders and try to figure out how each of them affect the graph visually. How does changing the features (above/below or solid/dashed) affect the equation of the inequality.

#### 2 Write an Equation for the graph

First show the students an inequality. Ask them how the sign of the inequality affects what the linear equation looks graphically. The answer is y ≤ 2x -4.

Look at the graph and write an equation for the line. Keep in mind the sign of the inequality.

#### 3 Graph a given equation

Instruct the students to graph the given inequality. Walk around the room making sure the students are drawing the correct features given the sign of the inequality.

DO NOT CLICK ON LINK. Create a graph of the following inequality. Use the appropriate line and shading. Once competed you may check your answer.

y ≥ -x + 4

#### 4 Solving a system of Inequalites Graphically

Have the students copy down the graph on a sheet up paper. Tell them to pick a point and plot it. Have them substitute their ordered pair into the blue inequality. Ask the students if their individual points make the inequality true. Ask them how do they know if the point is within the inequality or not. Have them plug in their points to both parts to discover where they need to shade within the two inequalities. Have the students collaborate with their neighbors to come up with a rule to which regions of the graph need to be shaded.

Copy down the graph of the inequalities onto graph paper. Select a point and determine weather the point is part of the two systems. (Hint: Try substituting your chosen ordered pair). Explain how you know your point is in the system or not. If your point is not find one that works in the two systems of inequalities.