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2.3.2: Solving Systems of Linear Inequalities

Read the scenario. Use the information to complete the problems that follow.

Taylor’s mother is fed up with all the dirty socks and T-shirts scattered on his bedroom floor. She made a bet with Taylor that if she could find 20 or more socks and T-shirts on his floor, Taylor would be grounded. If she finds less than that, Taylor doesn’t have to do dishes for a week.

1. What inequality represents how many socks and T-shirts found on the floor that will result in Taylor being grounded?

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2.3.2: Solving Systems of Linear Inequalities

2. Graph the inequality.

3. Taylor’s pretty sure he won’t have to do dishes for a week. What is the inequality that represents how many socks and T-shirts Taylor can have on the floor and still win the bet?

4. Graph this inequality on a separate coordinate plane.

5. What happens if there are exactly 20 socks and T-shirts on the floor? Who wins the bet?

2.3.2: Solving Systems of Linear Inequalities

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1. What inequality represents how many socks and T-shirts found on the floor that will result in Taylor being grounded?• Taylor’s mother thinks she’ll find 20 or more socks

and T-shirts.• The total number of items needs to be 20 or more.

Use the inequality symbol for “greater than or equal to” (≥) for this situation.

• Let x = the number of socks and y = the number of T-shirts.

x + y ≥ 20

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2.3.2: Solving Systems of Linear Inequalities

2. Graph the inequality.

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2.3.2: Solving Systems of Linear Inequalities

3. Taylor’s pretty sure he won’t have to do dishes for a week. What is the inequality that represents how many socks and T-shirts Taylor can have on the floor and still win the bet?• Taylor must have fewer than 20 socks and T-

shirts on his floor to win the bet.• Use the same variables, x and y. • x plus y must be less than 20 because Taylor’s

mother said she could find “20 or more.” Use the inequality symbol for “less than” (<) for this situation.

x + y < 20

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2.3.2: Solving Systems of Linear Inequalities

4. Graph this inequality on a separate coordinate plane.

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2.3.2: Solving Systems of Linear Inequalities

5. What happens if there are exactly 20 socks and T-shirts on the floor? Who wins the bet?• Taylor’s mother set up the situation so that if she

finds “20 or more” socks and T-shirts she wins; if there are exactly 20 of them, Taylor’s mother wins and Taylor is grounded. This can also be seen on the graph. The boundary for Taylor’s mother winning is solid and includes the cases where the total is 20, while the boundary for Taylor winning is non-inclusive (dashed), and does not include the total of 20.

2.3.2: Solving Systems of Linear Inequalities

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