Solving Systems of Linear Equations: Linear Combinations

Question 1

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together?5x + 13y = 23212x + 7y = 218The first equation can be multiplied by –13 and the second equation by 7 to eliminate y. The first equation can be multiplied by 7 and the second equation by 13 to eliminate y. The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.The first equation can be multiplied by 5 and the second equation by 12 to eliminate

Revolt · Accepted Answer

C: The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.

Question 2

What does 0 = 0 indicate about the solutions of the system?There are 0 solutions to the system.The solution to the system is (0, 0).There are solutions to the system at the x- and y-intercepts.There are infinitely many solutions to the system.

Revolt · Accepted Answer

D: There are infinitely many solutions to the system.

Question 3

Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?9x + 4y = 366x + 2.5y = 24Infinite solutions: 0x – 0y = 0No solutions: 0x + 15.5y = 144One solution: 0x + 0.5y = 0Two solutions: 0x – 0.5y = 60

Revolt · Accepted Answer

C: One solution: 0x + 0.5y = 0

Question 4

During one month of cell phone use, Noah used 200 anytime minutes and 400 text messages, and paid $80.00. The next month, he used 150 anytime minutes and 350 text messages, and paid $67.50. Which statement is true?Each text message costs 5 cents more than each anytime minute. Each anytime minute costs 10 cents more than each text message.A text message and an anytime minute each cost 25 cents.Each text message costs double the amount of an anytime minute.

Revolt · Accepted Answer

A: Each text message costs 5 cents more than each anytime minute.

Question 5

What values could A and B be for this system to have no solutions?A = 6, B = –4.5A = –10, B = –4.5A = –6, B = –3A = 10, B = –3

Revolt · Accepted Answer

A: A = 6, B = –4.5

Question 6

([___] , [___] )

Revolt · Accepted Answer

3

Question 7

([___] , [___] )

Revolt · Accepted Answer

-2

Question 8

A deli sells sliced meat and cheese. One customer purchases 4 pounds of meat and 5 pounds of cheese for a total of $30.50. A sandwich shop owner comes in and purchases 11 pounds of meat and 14 pounds of cheese for $84.50. The system of equations below represents the situation.

Revolt · Accepted Answer

The variable x represents the .: cost per pound of meat; The variable y represents the .: cost per pound of cheese; The deli charges $ .: 4.50 for a pound of meat

Question 9

The variable x represents the[___] .

Revolt · Accepted Answer

C: cost per pound of meat

Question 10

The variable y represents the[___] .

Revolt · Accepted Answer

D: cost per pound of cheese

Solving Systems of Linear Equations: Linear Combinations Answers

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