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1. |
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. |
Method II |
B. |
Both Method I and Method II are correct. |
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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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2. |
If you solve the following system of equations by elimination, which of the following is the best choice for the first step?
2x + y - z = 3
x + y + z = 5
x - 2y + z = 2
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A. |
Neither method will work. |
B. |
Both methods will work. |
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C. |
Add the first and second equations to eliminate the z variable. |
D. |
Subtract the second and third equation to eliminate the z variable. |
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Hint |
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3. |
Solve the system of equations by elimination.
2x + y - z = 3
x + y + z = 5
x - 2y + z = 2
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A. |
(1, 2, 1) |
B. |
(2, 1, 2) |
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C. |
(1, 1, 2) |
D. |
(2, 2, 1) |
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Hint |
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4. |
Find the values of x and y for which the matrix equation
 is true. |
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A. |
x = 1, y = -3 |
B. |
x = -3, y = -1 |
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C. |
x = -3, y = 1 |
D. |
x = -1, y = -3 |
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Hint |
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5. |
If A =  , find -2A. |
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A. |
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B. |
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C. |
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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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A. |
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B. |
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Hint |
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7. |
Find the inverse of  . |
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A. |
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B. |
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D. |
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Hint |
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8. |
Solve the systems of equations by using matrix equations. |
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A. |
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B. |
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D. |
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Hint |
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9. |
In shipping, an oversize package is one in which the sum of the length and girth exceeds 100 inches, and also one whose length alone exceeds 70 inches. Which of the following best represents this situation? |
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A. |
l + g > 100, l < 70 |
B. |
l + g < 100, g < 70 |
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C. |
l + g > 100, g < 70 |
D. |
l + g > 100, l > 70 |
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Hint |
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10. |
If the lumber mill can turn out 900 units of product each week and must produce 100 units of lumber and 400 units of plywood, graph the systems of inequalities. Let
x = units of lumber, and y = units of plywood. |
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A. |
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B. |
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Hint |
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11. |
Choose the best method to solve the system of equations x + y = 2
and y = 3x - 4. |
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A. |
Substitution |
B. |
Eliminate x |
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C. |
Eliminate y |
D. |
Graphing |
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Hint |
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12. |
The image of  after Rot180 · Ry-axis is the same as which other reflection, if the vertices are A(1,1), B(2,6), C(6,4)? |
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A. |
reflection over the y-axis |
B. |
reflection over the line y = x |
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C. |
none of these |
D. |
reflection over the x-axis |
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Hint |
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13. |
Solve the system of inequalities by graphing.
x + y  4
2x - y < 4
y  0 |
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B. |
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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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