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1. |
Solve the system of equations 2x + 3y = -7 and x - y = 4 by graphing. |
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Hint |
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2. |
If you use the substitution method to solve the system of equations
3x - 2y = 4 and x + y = 5, which of the following would be the best method?
Method I: Solve the second equation for x, and substitute 5 - y for x into the first equation.
Method II: Solve the second equation for y, and substitute 5 - x for y into the first equation.
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A. |
Both Method I and Method II are correct. |
B. |
Method II |
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C. |
Neither Method I nor Method II is correct. |
D. |
Method I |
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Hint |
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3. |
If you solve the following system of equations by substitution, which statement is true?
x = z
x - 2y + z = 6
2x + y - 2z = 1
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A. |
Both methods will work. |
B. |
You can substitute z for x into the second and third equations. |
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C. |
Neither method will work. |
D. |
You can substitute x for z into the second and third equations. |
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Hint |
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4. |
In 1999 Bob scored 824 points as a college basketball player by hitting 372 of his attempts. If he made 60% of his 200 3-point field goal attempts, how many 1-, 2-, and 3-point field goal baskets did he make? |
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A. |
(40, 120, 212) |
B. |
(120, 40, 212) |
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C. |
(212, 40, 120) |
D. |
(40, 212, 120) |
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Hint |
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5. |
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Hint |
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6. |
Suppose the triangle ABC with vertices A(1, 2), B(4, 3) and C(-1, 5) is translated 2 units right and 3 units down. Use the translation matrix to find the vertices for A'B'C', the translated image of the triangle. |
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Hint |
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7. |
Find the value of  . |
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A. |
3 |
B. |
17 |
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C. |
-17 |
D. |
-3 |
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Hint |
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8. |
Solve the systems of equations by using matrix equations. |
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9. |
The profit for each unit of lumber is $40 and the profit for each unit of plywood is $60. Write a profit function P(x, y) if x = the number of units of lumber and y = the number of units of plywood. |
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A. |
P(x, y) = 60x + 40y |
B. |
P(x, y) = 40x - 60y |
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C. |
P(x, y) = 60x - 40y |
D. |
P(x, y) = 40x + 60y |
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Hint |
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10. |
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A. |
impossible |
B. |
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Hint |
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11. |
The quadrilateral with vertices A(-1,5), B(2,7), C(4,5) and D(3,3) is reflected over the line y = x . Find the image of the quadrilateral after the reflection. |
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Hint |
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12. |
Solve the system of inequalities by graphing.
2x + y  3
2x + y  -2
y 4
x < 1 |
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B. |
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Hint |
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13. |
Find the maximum value of f(x, y) =  x - 4y for the system of inequalities.
2x + y 3
2x + y -2
y 4
x < 1 |
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A. |
-3 |
B. |
-16 |
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C. |
16 |
D. |
-17 |
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Hint |
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14. |
Sam has $10,000 to deposit in two different savings accounts. He wants at least $3,000 in the account that earns 3% interest. He wants no less than $5,000 in the account with 7% interest. Write a system of inequalities to represent this situation. |
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A. |
x 3000
y 5000
x + y 10,000 |
B. |
x 5000
y 3000
x + y 10,000 |
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C. |
x 3000
y 5000
x + y 10,000 |
D. |
x 3000
y 5000
x + y 10,000 |
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Hint |
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