Lesson 25

Representing Systems of Inequalities

• Let’s find and represent solutions to situations involving inequalities.

25.1: Which One Doesn’t Belong: Splash Zone!

Which one doesn't belong?

A: Clare’s family wants to

• spend at least 4 hours at the amusement park
• spend more time in the Splash Zone than riding rides

• be at the amusement park from 4 p.m. to 8 p.m.
• spend most of their time riding rides

C: Priya’s family wants to

• spend 2 hours at Splash Zone
• 2 hours riding rides

D: Diego’s family wants to

• spend no more than 6 hours at the amusement park
• spend at least twice as long riding rides as they spend at Splash Zone

25.2: Amusing Solutions

For each family, let $$x$$ be the amount of time each family spends riding rides, and $$y$$ be the amount of time each family spends at the Splash Zone.

List one or more ordered pairs $$(x, y)$$ that would fit the constraints. If you can only list one, explain why you can only list one.

1. Clare’s family wants to spend at least 4 hours at the amusement park, and they want to spend more time in the Splash Zone than riding rides.
2. Jada’s family wants to be at the amusement park from 4 p.m. to 8 p.m., and they want to spend most of their time riding rides.
3. Priya’s family wants to spend 2 hours at Splash Zone and 2 hours riding rides.
4. Diego’s family wants to spend no more than 6 hours at the amusement park, and they want to spend at least twice as long riding rides as they spend at Splash Zone.

25.3: Which Section?

1. The graph shows the lines $$y = x + 1$$ and $$y = \text{-} x - 2$$. Which line represents $$y = x + 1$$?
2. For each of the 4 regions, write a coordinate pair for a point in that region.
3. Change the equations represented by the lines into inequalities so that the region labeled as A is shaded by both inequalities.
1. $$y \underline{\hspace{.5in}} x + 1$$
2. $$y \underline{\hspace{.5in}} \text{-}x - 2$$
4. Use the coordinate pairs you chose for region A to check your inequalities.