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Question : Identify systems with no solution and systems with infinitely many solutions : 2151791

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.

1) x + y = 8

x + y = 7

A) {(0, 15)}

B) {(8, 7)}

C) {(x, y)|x + y = 8}

D) ∅

2) y = 37 - 8x

8x + y = 61

A) {(28, 29)}

B) {(32, 5)}

C) {(x, y)|8x + y = 37}

D) ∅

3) y = 10 - 2x

8x + 4y = 40

A) {(0, 10)}

B) {(5, 0)}

C) {(x, y)|2x + y = 10}

D) ∅

4) (4x + y = 11)(8x + 2y = 22)

A) {(0, 11)}

B) {(5, -9)}

C) {(x, y)|4x + y = 11}

D) ∅

5) x + y = -4

x - y = 13

A) {(4.5, -8.5)}

B) {(4.5, 8.5)}

C) {(x, y)|x + y = -4}

D) ∅

6) 3x - 5y = 5

-9x + 15y = -20

A) {(3, 4)}

B) {((2/5), - (2/3))}

C) {(x, y)|3x - 5y = 5 }

D) ∅

7) x + 7y = 41

-5x + 6y = 41

A) {(-1, 6)}

B) {(-2, 7)}

C) {(x, y)|x + 7y = 41}

D) ∅

8) 2y = 6 - 4x

2x = 16 - 2y

A) {(2, -13)}

B) {(-5, 13)}

C) {(x, y)|4x + 2y = 6 }

D) ∅

9) x + 5y = -1

5x + 25y = -5

A) {(-1, 0)}

B) {(0, 0)}

C) {(x, y)|x + 5y = -1}

D) ∅

10) y = -6x - 5

-18x - 3y = 15

A) ∅

B) {(0, -5)}

C) {(x, y)|6x + y = -5}

D) {(0, 0)}

11) 3x + y = 2

4y = 8 - 12x

A) {((2/3), 0)}

B) {(0, 2)}

C) {(x, y)|3x + y = 2}

D) ∅

12) y = (1/5)x + 6

x - 5y = -30

A) {(0, 6)}

B) {(-30, 0)}

C) {(x, y)|x - 5y = -30}

D) ∅

13) 7x - 5y = 9

-28x + 20y = -18

A) {(4, 2)}

B) {((7/3), - (5/3))}

C) {(x, y)|7x - 5y = 9}

D) ∅

14) (x/3) + (y/3) = -3

x - y = 1

A) {(x, y)|x - y = 1 }

B) {(-5, -4)}

C) {(-4, -5)}

D) ∅

15) (x/5) + (y/15) = 1

(x/3) - (y/9) = 0

A) {((5/2), (15/2))}

B) {((15/2), (5/2))}

C) {(x, y)|(x/5) + (y/15) = 1}

D) ∅

Solve the problem.

16) The sum of two numbers is 6. If one number is subtracted from the other, their difference is -12. Find the numbers.

A) -3, 9

B) 3, 9

C) 8, -2

D) -3, -9

17) One number is 1 less than a second number. Twice the second number is 18 less than 4 times the first. Find the two numbers.

A) 11 and 12

B) 9 and 10

C) 10 and 11

D) -11 and -10

18) One number is 1 less than a second number. Twice the second number is 20 more than 4 times the first. Find the two numbers.

A) 8 and 9

B) -10 and -9

C) -9 and -8

D) -8 and -7

19) Two cars leave a city and head in the same direction. After 3 hours, the faster car is 27 miles ahead of the slower car. The slower car has traveled 144 miles. Find the speeds of the two cars.

A) 48 mph and 57 mph

B) 39 mph and 48 mph

C) 90 mph and 99 mph

D) 50 mph and 59 mph

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.

20) How many binoculars must be produced and sold for the company to break even?

A) 2250 binoculars

B) 2700 binoculars

C) 750 binoculars

D) 1500 binoculars

21) At the break-even point both cost and revenue are what?

A) $2700

B) $750

C) $1500

D) $2250

22) More than how many binoculars must be produced and sold for the company to have a profit gain?

A) 750 binoculars

B) 1500 binoculars

C) 2700 binoculars

D) 2250 binoculars

23) Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

A) 1500 binoculars

B) 2700 binoculars

C) 2250 binoculars

D) 750 binoculars

24) Use the revenue and cost functions to write the profit function from producing and selling x binoculars.

A) P(x) = 2x + 1500

B) P(x) = 4x + 1500

C) P(x) = 4x - 1500

D) P(x) = 2x - 1500

25) Is there a profit when 605 binoculars are produced?

A) No

B) Yes

26) Is there a profit when 812 binoculars are produced?

A) Yes

B) No

27) What is the profit when 840 binoculars are produced?

A) $1860

B) $4860

C) $180

D) $3180