Calculus math problems

Solve the system of equations. If the system has no solution, say that it is inconsistent.

x = 4, y = 2; (4, 2)

x = 2, y = 4; (2, 4)

x = 2, y = 3; (2, 3)

inconsistent

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QUESTION 2

Solve the problem.

The Paperback Trader is a book store that takes in used paperbacks for 20% of their cover price and sells them for 50% of their cover price. Pat brings in a stack of 16 paperback books to trade and gets $17.50 credit. Some of the books had a cover price of $7.97, the rest $3.97. She wants to get some Tom Clancy books having a cover price of $7.97. How many $7.97 books did she bring in and how many Clancy books can she get without paying any additional cash?

10 $7.97 books, 2 Clancy books

6 $7.97 books, 4 Clancy books

6 $7.97 books, 5 Clancy books

6 $7.97 books, 2 Clancy books

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QUESTION 3

Solve the system of equations by elimination.

x = -3, y = 10; (-3, 10)

x = -10, y = 3; (-10, 3)

x = 3, y = -10; (3, -10)

x = 10, y = -3; (10, -3)

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QUESTION 4

Solve the problem.

An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?

132 mi

147 mi

153 mi

168 mi

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QUESTION 5

Solve the system of equations by substitution.

x = 7, y = 12; (7, 12)

x = 12, y = -2; (12, -2)

x = 3, y = 7; (3, 7)

x = -2, y = 3; (-2, 3)

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QUESTION 6

Solve the system of equations by elimination.

x = 3, y = 8; (3, 8)

x = 3, y = -11; (3, -11)

x = 8, y = -11; (8, -11)

x = 8, y = 11; (8, 11)

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QUESTION 7

Solve the system of equations by substitution.

x = 2, y = 11; (2, 11)

x = 9, y = -11; (9, -11)

x = 9, y = 2; (9, 2)

x = 2, y = -11; (2, -11)

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QUESTION 8

Solve the system of equations. If the system has no solution, say that it is inconsistent.

x = -4y + 5, where y is any real number

or {(x, y) |x = -4y + 5, where y is any real number}

y = -4x + 5, where x is any real number

or {(x, y) | y = -4x + 5, where x is any real number}

y = 4x + 5, where x is any real number

or {(x, y) | y = 4x + 5, where x is any real number}

inconsistent

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QUESTION 9

Solve the system of equations by elimination.

x = 1, y = 1; (1, 1)

x = 0, y = 0; (0, 0)

x = 0, y = 1; (0, 1)

x = 1, y = 0; (1, 0)

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QUESTION 10

Solve the system of equations. If the system has no solution, say that it is inconsistent.

x = -8, y = 0; (-8, 0)

x = 0, y = 0; (0, 0)

y = - - 4, where x is any real number

or {(x, y) | y = - - 4, where x is any real number}

inconsistent

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QUESTION 11

Solve the system of equations. If the system has no solution, say that it is inconsistent.

x = 9, y = 2; (9, 2)

x = , y = ;

x = -9, y = -8; (-9, -8)

inconsistent

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QUESTION 12

Solve the problem.

A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many of them were adults?

16 adults

24 adults

29 adults

10 adults

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QUESTION 13

Solve the system of equations. If the system has no solution, say that it is inconsistent.

x = -8, y = -4; (-8, -4)

x = 0, y = -12; (0, -12)

x = 0, y = 0; (0, 0)

inconsistent

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QUESTION 14

Solve the system of equations by elimination.

x = 0, y = -4; (0, -4)

x = -4, y = 0; (-4, 0)

x = 0, y = 4; (0, 4)

x = 4, y = 0; (4, 0)

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QUESTION 15

Solve the system of equations by elimination.

x = -6, y = 5; (-6, 5)

x = 11, y = -11; (11, -11)

x = 5, y = -5; (5, -5)

x = -5, y = 5; (-5, 5)

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QUESTION 16

Solve the system of equations by elimination.

x = -5, y = 18; (-5, 18)

x = 18, y = -5; (18, -5)

x = -18, y = 6; (-18, 6)

x = -18, y = 5; ( -18, 5)

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QUESTION 17

Verify that the values of the variables listed are solutions of the system of equations.

x = -2, y = -3

solution

not a solution

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QUESTION 18

Solve the system of equations by substitution.

x = 0, y = 0; (0, 10)

x = 10, y = 10; (10, 10)

x = 10, y = 0; (10, 0)

x = 0, y = 10; (0, 10)

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QUESTION 19

Verify that the values of the variables listed are solutions of the system of equations.

x = -3, y = 4

solution

not a solution

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QUESTION 20

Solve the system of equations by elimination.

x = 3, y = 9; (3, 9)

x = 2, y = 9; (2, 9)

x = 3, y = 8; (3, 8)

x = 2, y = 8; (2, 8)

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QUESTION 21

Solve the system of equations by substitution.

x = 3, y = 8; (3, 8)

x = 2, y = 9; (2, 9)

x = 3, y = 9; (3, 9)

x = 2, y = 8; (2, 8)

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QUESTION 22

Solve the system of equations. If the system has no solution, say that it is inconsistent.

x = -1, y = ;

y = - x + 12, where x is any real number

or {(x, y) | y = - x + 12, where x is any real number}

x = 0, y = 12; (0, 12)

inconsistent

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QUESTION 23

Solve the system of equations by substitution.

x = 0, y = 1; (0, 1)

x = 1, y = 1; (1, 1)

x = 1, y = 0; (1, 0)

x = 0, y = 0; (0, 0)

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QUESTION 24

Solve the problem.

A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 7 slices of pizza and 4 soft drinks for $31.49. The second group bought 5 slices of pizza and 6 soft drinks for $26.61. How much does one slice of pizza cost?

$3.25 per slice of pizza

$1.81 per slice of pizza

$3.75 per slice of pizza

$1.31 per slice of pizza

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QUESTION 25

Solve the system of equations by substitution.

x = 3, y = -3; (3, -3)

x = -3, y = -3; (-3, -3)

x = -3, y = 3; (-3, 3)

x = -3, y = 0; (-3, 0)

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