System of Multiple Linear Equations

Jamaurrie is throwing a summer party. He has a 75 dollar spending limit on meat and a 40 dollar spending limit on salads. The cost per pound is shown. - Chicken: $1.99 per pound - Steak: $4.49 per pound - Potato Salad: $1.49 per pound - Macaroni Salad: $2.99 per pound Jamaurrie plans to purchase c pounds of chicken, s pounds of steak, p pounds of potato salad, and m pounds of macaroni salad. Which equations represent the possible number of pounds he can buy?

• 1.99c + 4.49s = 40 and 1.49p + 2.99m = 75

• 1.99c + 4.49s = 75 and 1.49p + 2.99m = 40

• (1.99 + 4.49) (c + s) = 40 and (1.49 + 2.99) (p + m) = 75

• (1.99 + 4.49) (c + s) = 75 and (1.49 + 2.99) (p + m) = 40

Alex and Joanna started with the same number of football cards in their collections. Alex collected 5 cards per week and now has 45 cards. Joanna collected 3 cards per week and now has 31 cards. Let x represent the number of cards they began with, and let y represent the number of weeks. Which system of equations represents this situation?

• x + 5y = 45 x + 3y = 31

• x + y = 31 5x + 3y = 45

• 8y = 76 x + 31 = 45

• y + 31 = 76 8x = 45

A system of linear equations is given. x − y = 5 x + y = −5 Which statement is TRUE about the solution of the system of linear equations?

• The solution is (0, −5) because this ordered pair represents the y-intercepts for both equations.

• The solution is (−5, 0) because this ordered pair represents the x-intercepts for both equations.

• The solution is (0, −5) because this ordered pair represents the point of intersection for both lines in the system of linear equations.

• The solution is (−5, 0) because this ordered pair represents the point of intersection for both lines in the system of linear equations.

Jontez and KD sold 100 tickets for a fundraiser. KD sold 24 more tickets than Jontez. The equations that represent the scenario are x + y = 100 and x − y = 24. Which statement is TRUE about the number of tickets sold?

• There is 1 solution to the system of equations, which shows that KD sold 62 tickets.

• There is 1 solution to the system of equations, which shows that KD sold 76 tickets.

• There are infinitely many solutions to the system of equations because there are infinitely many combinations of tickets sold that have a sum of 100.

• There are infinitely many solutions to the system of equations because there are infinitely many combinations of tickets sold that have a difference of 24.

The system of linear equations represents the total sales an airline wants to have for 2 different flights represented by the number of economy seats sold, x, and first class seats sold, y. 400x + 600y = 8,000 400x + 600y = 16,000 What statement BEST explains the number of solutions for the system of linear equations?

• The system of linear equations has 1 solution because 400x + 600y can equal 2 different numbers.

• The system of linear equations has no solutions because 400x + 600y cannot equal 2 different numbers.

• The system of linear equations has 1 solution because the second equation is a multiple of the first equation.

• The system of linear equations has no solutions because the second equation is a multiple of the first equation.

Brittany, Keondra, and Aniyah are heading along the same straight sidewalk towards a park gate. The graph shows Brittany's distance, y, in feet from the gate after x minutes. The equation y = −300x + 700 represents Keondra's distance, y, in feet from the gate after x minutes. The equation y = −300x + 600 represents Aniyah's distance, y, in feet from the gate after x minutes. Which statement is TRUE about when Brittany, Keondra, and Aniyah are predicted to pass by each other?

• Keondra and Brittany will pass by each other before Aniyah and Brittany will pass by each

  other, but Aniyah and Keondra will not pass by each other.

• Aniyah and Brittany will pass by each other before Keondra and Brittany will pass by each

  other, but Aniyah and Keondra will not pass by each other.

• Keondra and Brittany will pass by each other, then Aniyah and Brittany will pass by each other,

  and then Aniyah and Keondra will pass by each other.

• Aniyah and Brittany will pass by each other, then Keondra and Brittany will pass by each other,

  and then Aniyah and Keondra will pass by each other.

Which THREE systems have a solution with an x-value that is less than the y-value?

• 6x -8y = 6 and

  y = 2x + 8

• 
• -3x + 5y = -5 and

  x - 7y = -25

• 
• 6x - 8y = 6 and

  y = 2x + 8

Which TWO systems of equations have exactly one solution?

• 6x – 3y = 3 2x – y = 4

• y = –2x – 8 y = x + 1

• 6x – 3y = 12 2x – y = 4

• x – 4y = 8 3x + 2y = 10

• y = 2x + 1 y = 2x – 2

Lenwood has $150 to spend on a barbecue. He plans to buy chicken at $2.50 per pound and ribs at $6.50 per pound. Which equation represents the constraints on his purchase of c pounds of chicken and r pounds of ribs?

• 2.50c + 6.50r = 150

• 2.50c + 6.50r = 150 – 6.50 – 2.50

• (6.50 + 2.50) (c + r) = 150

• (6.50 – 2.50) (c + r) = 150 – 6.50 – 2.50

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740

• S + A = 530
  4S + 3A = 1740

• S + A = 1740
  3S + 4A = 530

• S + A = 1740
  4S + 3A = 530