Grade 8 | Unit 4 | Lesson 12: Systems of Equations | Practice Problems

Here is the graph for one equation in a system of equations: Description:

Graph of a line in the xy plane, origin O, with grid. Horizontal axis, scale negative 6 to 6, by 1’s. Vertical axis, scale negative 6 to 6, by 1’s. The line crosses the y axis at 4. It passes through the point 4 comma 1.

Write a second equation for the system so it has infinitely many solutions.

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Andre is in charge of cooking broccoli and zucchini for a large group. He has to spend all $17 he has and can carry 10 pounds of veggies. Zucchini costs $1.50 per pound and broccoli costs $2 per pound. One graph shows combinations of zucchini and broccoli that weigh 10 pounds and the other shows combinations of zucchini and broccoli that cost $17. Description:

The graph of two intersecting lines in the xy plane. The first line slants downward and right and passes through the point 4 comma 5 point 5. The second line slants downward and to the right and passes through the point 5 comma 5. The lines intersect at the point 6 comma 4.

Name one combination of veggies that weighs 10 pounds but does not cost $17.

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Andre is in charge of cooking broccoli and zucchini for a large group. He has to spend all $17 he has and can carry 10 pounds of veggies. Zucchini costs $1.50 per pound and broccoli costs $2 per pound. One graph shows combinations of zucchini and broccoli that weigh 10 pounds and the other shows combinations of zucchini and broccoli that cost $17. Description:

The graph of two intersecting lines in the xy plane. The first line slants downward and right and passes through the point 4 comma 5 point 5. The second line slants downward and to the right and passes through the point 5 comma 5. The lines intersect at the point 6 comma 4.

Name one combination of veggies that costs $17 but does not weigh 10 pounds.

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Andre is in charge of cooking broccoli and zucchini for a large group. He has to spend all $17 he has and can carry 10 pounds of veggies. Zucchini costs $1.50 per pound and broccoli costs $2 per pound. One graph shows combinations of zucchini and broccoli that weigh 10 pounds and the other shows combinations of zucchini and broccoli that cost $17. Description:

The graph of two intersecting lines in the xy plane. The first line slants downward and right and passes through the point 4 comma 5 point 5. The second line slants downward and to the right and passes through the point 5 comma 5. The lines intersect at the point 6 comma 4.

How many pounds each of zucchini and broccoli can Andre get so that he spends all $17 and gets 10 pounds of veggies?

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