Linear Systems Graphing and Applications

Heather owns a successful flower shop and is hired to make flower arrangements for several weddings in her community. She charges the same flat fee for each wedding (fixed cost). In addition to the flat fee she charges a certain amount for each arrangement she creates. If the cost is $2500 for a wedding with 50 flower arrangements and $3250 for a wedding with 75 flower arrangements, find the fixed cost and the cost per flower arrangement.

• Fixed Cost: $1000

  Cost per Flower Arrangement: $25

• Fixed Cost: $500

  Cost per Flower Arrangement: $30

• Fixed Cost: $1000

  Cost per Flower Arrangement: $30

• Fixed Cost: $1500

  Cost per Flower Arrangement: $10

Solve the system by graphing.

6x + 4y = -12

3x + 2y = 1

• (1, 1)

• (0, 0)

• No Solution

• Infinitely Many Solutions

Give the solution to the system.

• (3,1)

• (1,3)

• (-1,3)

• (1, -3)

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? Let "c" represent the # of people who ordered chicken and "s" represent those who ordered steak.

• c + s = 6
  14.80c + 17s = 91

• c + s = 91
  14.80c + 17s = 6

• c + s = 6
  14.80s + 17c = 91

• c + s = 91
  14.80s+ 17c = 6

Beyonce wanted to host a barbecue for Spring Break next week. A package of hot dogs cost $1.60, and a package of hamburgers costs $5. Beyonce bought a total of 8 packages of meat and spent $23 total. Write a system for this situation. Assume "x" represents # of hot dog packages and "y" represent # of hamburger packages.

• x + y = 8
  1.60x + 5y = 23

• x + y = 23
  1.60x + 5y = 8

• x + y = 8
  1.60y + 5x = 23

• x + y = 23
  1.60y + 5x = 8

Captain America wanted to put on a community bake sale. He purchased 12 pounds of sugar and 15 pounds of flour. Iron Man noticed that they needed more ingredient and purchased 4 pounds of sugar and 10 pounds of flour. Iron Man spent $4.60, and Captain America spent $9.30. Let "s" represent the cost per pound of sugar and "f" represent the cost per pound of flour.

• 12s + 15f = 9.30
  4s + 10f = 4.60

• 12s + 15f = 4.60
  4s + 10f = 9.30

• 12f + 15s = 9.30
  4f + 10s = 4.60

• 12f + 15s = 4.60
  4f + 10s = 9.30

The graph of the function y = 1/2x – 3 is shown. If this line is shifted up 7 units what is the new equation?

• y = 7/2x – 3

• y = 1/2x + 7

• y = 1/2x + 4

• y = -1/2x +4

What is the solution to this system of equations?

• (1,0)

• (-3, -1)

• (-1,-3)

• (1,3)

Solve by graphing.
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Solve this system of equations by graphing.

y = 1/2x + 2

y = -3x + 9

• (2, 3)

• (-2, -3)

• (3, 2)

• (-3, 2)