A1.1.2.2.1 - Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination. Note: Limit systems to two linear equations.

Anna burned 15 calories per minute running for x minutes and 10 calories per minute hiking for y minutes. She spent a total of 60 minutes running and hiking and burned 700 calories. The system of equations shown below can be used to determine how much time Anna spent on each exercise. 15x + 10y = 700 x + y = 60 What is the value of x, the minutes Anna spent running? A. 10 B. 20 C. 30 D. 40 Answer: B

A1.1.2.2.2 - Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear equations.

Samantha and Maria purchased flowers. Samantha purchased 5 roses for x dollars each and 4 daisies for y dollars each and spent $32 on the flowers. Maria purchased 1 rose for x dollars and 6 daisies for y dollars each and spent $22. The system of equations shown below represents this situation. 5x + 4y = 32 x + 6y = 22 Which statement is true? A. A rose costs $1 more than a daisy. B. Samantha spent $4 on each daisy. C. Samantha spent more on daisies than she did on roses. D. Samantha spent over 4 times as much on daisies as she did on roses.

## A1.1.2.2 - Write, solve, and/or graph systems of linear equations using various methods.

## Key Vocabulary: Elimination Method, Equation, Linear Equation, Ordered Pair, Substitution, System of Linear Equations

## A1.1.2.2.1 - Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination. Note: Limit systems to two linear equations.

Anna burned 15 calories per minute running for x minutes and 10 calories per minute hiking for y minutes. She spent a total of 60 minutes running and hiking and burned 700 calories. The system of equations shown below can be used to determine how much time Anna spent on each exercise.

15x + 10y = 700

x + y = 60

What is the value of x, the minutes Anna spent running?

A. 10

B. 20

C. 30

D. 40

Answer: B

## A1.1.2.2.2 - Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear equations.

Samantha and Maria purchased flowers. Samantha purchased 5 roses for x dollars each and 4 daisies for y dollars each and spent $32 on the flowers. Maria purchased 1 rose for x dollars and 6 daisies for y dollars each and spent $22. The system of equations shown below represents this situation.

5x + 4y = 32

x + 6y = 22

Which statement is true?

A. A rose costs $1 more than a daisy.

B. Samantha spent $4 on each daisy.

C. Samantha spent more on daisies than she did on roses.

D. Samantha spent over 4 times as much on daisies as she did on roses.

Answer: A

## Additional Resources:

PDESAS Algebra I Module 2 ResourcesKhan Academy - Systems of Equations