Finding a Solution to Systems of Equations

Point of intersection:​ (a)   Break-even point: ​ (b)   bookmarks.

At least ​ (c)   bookmarks must be sold to make a profit

• (25, 60)

• (60,25)

• (0,0)

• (0,40)

• 60

• 40

• 0

• 25

• 26

Point of intersection:​ (a)   Break-even point: ​ ​ (b)   bumper stickers.

At least ​ (c)   bumper stickers must be sold to make a profit

• (45, 225)

• (225,45)

• (0,0)

• (0,85)

• 225

• 85

• 0

• 45

• 46

Shawn started walking from home to school just as his brother Dante was leaving school to walk home. The distance from their home to school is 11,680 feet. Dante was walking at a slow pace averaging about 292.5 feet per minute. Shawn, who was excited to get to class, was walking more quickly, averaging about 437.5 feet per minute. Assume they both left at the same time and maintained their rate of speed for the entire trip. Sean and Dante will meet in (a)   when they are ​ (b)   feet from home. ​

• 16

• 7000

• 11,680

• 292.5

• 437.5

Damien has saved all of his allowance for a year to pay for guitar lessons and has a total of $550 in savings. His friend Kira is just starting to save and has $50 so far. Each week Damien will pay Kira $25 for a guitar lesson and Kira will save the money in her savings account. In how many weeks will their accounts have the same amount

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, 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

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

• 5q + 2z = 1.32
  1z = 0.75

• 5q + 2z = 1.32
  3q + 1z = 0.75

• q + z = 1.32
  q + z = 0.75

• 5q + 2z = 0.75
  3q + 1z = 1.32

Solve the system of equations:
−6x + 6y = 0
9x − 8y = 4 

• (4, −9)
  

• Infinite number of solutions 

• (−9, 4)
  

• (4, 4) 

On the first night, the Movie House Theater sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Find the price of an adult ticket and the price of a child ticket.

• Adult $13
  Child $5

• Adult $10
  Child $6

• Adult $8
  Child $16

• Adult $12
  Child $13

Solve by elimination:
-9x-4y=-20

5x+4y=4

• (-4,4)

• (4,4)

• (4,-4)

• (-4,-4)

To eliminate a variable in the system, should you add the equations or subtract the equations?

• Add

• Subtract

• Neither