Modeling With Systems of Equations

The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students.

Write the equations needed to solve the problem: (8.EEI.C.8d)

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8.EEI.C.8d

8.EEI.C.8.d

Kai and Nora are trying to solve a system of two linear equations but they find that there are no solutions. What can they conclude about the graphs of the two equations they are trying to solve? (8.EEI.C.8c)

• The lines representing the equations have the same slope and the same y-intercept.

• The lines representing the equations have the same slope and different y-intercepts.

• The lines representing the equations have different slopes and the same y-intercept.

• The lines representing the equations have different slopes and different y-intercepts.

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8.EEI.C.8.c

The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? (8.EEI.C.8d)

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8.EEI.C.8.d

The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a bus carry? (8.EEI.C.8d)

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8.EEI.C.8.d

Anika, Aiden, and Elijah are trying to determine the number of solutions for a system of equations they encountered while studying. The equations are as follows: y=\frac{2}{3}x-6 y=\frac{2}{3}x+3 How many solutions does this system have, and why?

• There are no solutions because the slopes and y-intercepts are the same.

• There are infinitely many solutions because the slopes and y-intercepts are the same.

• There are no solutions because the slopes are the same and the y-intercepts are different.

• There are infinitely many solutions because the slopes are the same and the y-intercepts are different.

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8.EEI.C.8c

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8.EEI.C.8b

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8.EEI.C.8b

Solve the system of equations using substitution, elimination, or inspection. Mark if the system will have one solution, no solution, or infinitely many solutions and justify your reasoning. (8.EEI.C.8b) y=\frac{1}{2}x-1;\ y=3x+2

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8.EEI.C.8b

Jerry buys gray modeling clay and pink modeling clay. Gray modeling clay cost $4 per pound. Pink modeling clay costs $5 per pound. Jerry orders a total of 14 pounds of modeling clay for $60. To represent this situation, Jerry writes the system of equations shown (8.EEI.C.8b). Graph the linear equations on page 4 of the paper test.

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8.EEI.C.8b

• 10

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• 8

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