IM 8.4.16

IM 8.4.16

Solving Problems with Systems of Equations

• Let's solve some more systems!

Multiple Choice

Solve the following system:

 $y\ =\ 1x\ +\ 15$  

 $2x\ +\ 3y\ =\ 10$  

• (7,8)

• (8,7)

• (-7,8)

• (-7,-8)

Multiple Choice

Solve for x and y

3x + 2y = 16

y = 19 - 7x

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

We can create systems based off of stories.

• Write two equations that represent the situation.

Multiple Choice

A car is driving towards home at 0.5 miles per minute. If the car is 4 miles from home at t=0, which of the following can represent the distance that the car has left to drive?

• 0.5t

• 4+0.5t

• 4-0.5t

• 4(0.5t)

Multiple Choice

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450
• 3x + 2y = 450
  2x + 4y = 315
• 2x + 2y = 315
  3x + 4y = 450

Multiple Choice

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5
  x+y=87
• 1.5x+0.5y=78.5
  1.5x+0.5y=87
• x+y=78.5
  1.5x+0.5y=87
• x+y=78.5
  x+y=87

Multiple Choice

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined.

1.5x+0.5y=78.5

y=87 -x

Solve the system

• (35,52)

• (52,35)

• (-35,-52)

• (-52,-35)

Multiple Choice

Two friends live 7 miles apart. One Saturday they set out to ride toward each other. One rides 0.2 miles per minute. and the other rides at 0.15 miles per minute. Which system of equations represents this situation?

• y = 0.2x

  y= -0.15x + 7

• y = -0.2x

  y= -0.15x - 7

• y = -0.2x

  y= -0.15x + 7

Multiple Choice

Students are selling grapefruits and apples for a fundraiser. The grapefruits cost $1 each and a bag of apples costs $10. They sell 100 items and make $307. What would be a system of equations that represents this situation?

• x+y = 307

  x+y =100

• x+10y = 307

  x+y =100

• x+10y = 100

  x+y =307

Multiple Choice

Students are selling grapefruits and apples for a fundraiser. The grapefruits cost $1 each and a bag of apples costs $10. They sell 100 items and make $307. How many grapefruits did they sell?

x+10y = 307

x+y =100

• 14

• 77

• 107

• 23

Multiple Choice

Jada earns $7 per hour mowing her neighbors lawn. Andre spends $3 on gas to show up to babysit plus an additional $8 per hour. Write a system of equations to represent their income.

• y= 7x

  y= 8x +3

• y= 7x + 3

  y= 8x

• y= 7x

  y= 8x - 3