Solving Systems of Linear Equations: Linear Combinations

Question 1

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?

Revolt · Accepted Answer

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

Question 2

Complete the steps used to solve a system of linear equations by substituting the value of y into one of the original equations to find the value of x.

Revolt · Accepted Answer

3.5; -2

Question 3

([___] , [___] )

Revolt · Accepted Answer

-2

Question 4

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

✔ cost per pound of meat; 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 5

What values could A and B be for this system to have no solutions?

Revolt · Accepted Answer

A = 6, B = –4.5

Question 6

The solution is [___].

Revolt · Accepted Answer

(–2, 3)

Question 7

What does 0 = 0 indicate about the solutions of the system?

Revolt · Accepted Answer

There are infinitely many solutions to the system.

Question 8

Dawn has been using two bank accounts to save money for a car. The difference between account 1 and account 2 is $100. If she uses 3/8 of account 1 and 7/8 of account 2, Dawn will have a down payment of $2,000. Solve the system of equations to find the total amount of money Dawn has in each account.

Revolt · Accepted Answer

✔ 1,670; Dawn has $ in account 1 and $ in account 2.: 1,670; Dawn has $ in account 1 and $ in account 2.: 1,570

Question 9

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 = 24

Revolt · Accepted Answer

One solution: 0x + 0.5y = 0

Question 10

Henrique began to solve a system of linear equations using the linear combination method. His work is shown below:3(4x – 7y = 28) → 12x – 21y = 84–2(6x – 5y = 31) → –12x + 10y = –62 12x – 21y = 84+ –12x + 10y = –62 –11y = 22y = –2

Revolt · Accepted Answer

3; -2

Solving Systems of Linear Equations: Linear Combinations Answers

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