A1.1.3.2.1 - Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities.

Graph the system of inequalities is shown below. y < x – 6 y > –2x

A1.1.3.2.2 - Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear inequalities.

Tyreke always leaves a tip of between 8% and 20% for the server when he pays for his dinner. This can be represented by the system of inequalities shown below, where y is the amount of tip and x is the cost of dinner. y > 0.08x y < 0.2x Which of the following is a true statement? A. When the cost of dinner ( x) is $10, the amount of tip ( y) must be between $2 and $8. B. When the cost of dinner ( x) is $15, the amount of tip ( y) must be between $1.20 and $3.00. C. When the amount of tip ( y) is $3, the cost of dinner ( x) must be between $11 and $23. D. When the amount of tip ( y) is $2.40, the cost of dinner ( x) must be between $3 and $6.

## A1.1.3.2 - Write, solve, and/or graph systems of linear inequalities using various methods.

## Key Vocabulary: Systems of Linear Inequalities

## A1.1.3.2.1 - Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities.

Graph the system of inequalities is shown below.

y < x – 6

y > –2x

## A1.1.3.2.2 - Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear inequalities.

Tyreke always leaves a tip of between 8% and 20% for the server when he pays for his dinner. This can be represented by the system of inequalities shown below, where y is the amount of tip and x is the cost of dinner.

y > 0.08x

y < 0.2x

Which of the following is a true statement?

A. When the cost of dinner ( x) is $10, the amount of tip ( y) must be between $2 and $8.

B. When the cost of dinner ( x) is $15, the amount of tip ( y) must be between $1.20 and $3.00.

C. When the amount of tip ( y) is $3, the cost of dinner ( x) must be between $11 and $23.

D. When the amount of tip ( y) is $2.40, the cost of dinner ( x) must be between $3 and $6.

## Answer: B

## Additional Resources:

Khan Academy - videos of systems of inequalitiesRegent's Prep Practice