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1. |
A graph of a system of three linear equations in three variables is shown below. How many solutions does the system have? |
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A. |
0 |
B. |
1 |
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C. |
2 |
D. |
infinite number |
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Hint |
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2. |
Solve the system 4y – 6x + 8z = 13, 10y – 15x + 20z = 6, y – 5x + 2z = 5. |
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A. |
(-3, 1, 7) |
B. |
infinite solutions |
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C. |
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D. |
no solution |
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Hint |
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3. |
At a firm, there are three workers that are supposed to work a combined 110 hours per week. Worker 1 is supposed to work 5 hours more than worker 2, and worker 2 is supposed to work 15 hours more than worker 3. How long should each one work? |
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A. |
worker 1: 45worker 2: 35worker 3: 30 |
B. |
worker 1: 45worker 2: 40worker 3: 25 |
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C. |
worker 1: 40worker 2: 45worker 3: 25 |
D. |
worker 1: 42.5worker 2: 37.5worker 3: 30 |
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Hint |
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4. |
At a firm, there are three workers that are supposed to work a combined 110 hours per week. Worker 1 gets paid $10 per hour, worker 2 gets paid $12 per hour, and worker 3 gets paid $14 per hour. If the company wants their total income to be $1268, how many hours should each one work if worker 3 and worker 2 work for the same amount of hours? |
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A. |
worker 1: 54worker 2: 28worker 3: 28 |
B. |
worker 1: 44worker 2: 33worker 3: 33 |
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C. |
worker 1: 40worker 2: 35worker 3: 35 |
D. |
worker 1: 14worker 2: 48worker 3: 48 |
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Hint |
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5. |
What is true about a system of equations in three variables that has 1 solution? |
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A. |
planes intersect in one line |
B. |
planes have no points in common |
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C. |
planes intersect in the same plane |
D. |
planes intersect in one point |
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Hint |
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