Unit 6 Day 6 Progress Check

Remember the farm?
Unit 6 Day 6 - Systems Applications in STANDARD FORM

Multiple Choice

There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all.  Which system of equations represents the situation?

• x + y = 15
  4x + 2y = 44
• 4x + 2y = 15
  x + y = 44
• x = 2y + 44
  4x = y + 15
• 2x - 4y = 44
  x - y = 15

Multiple Choice

Elijah is thinking of two numbers.  Their sum is -10 and their difference is -2.  Which system of equations represents the situation?

• x - y = -10
  x + y = -2
• x = -2 
  y = 5
• x + y = -2
  x - y = -10
• x + y = -10
  x - y = -2

Multiple Choice

Lucy is thinking of two numbers.  The sum of the numbers is 100. One of the numbers is 20 more than 3 times the other.  Which system of equations represents the situation?

• x + y = 100

  y = 4x - 20

• x + y = 80

  y = 3x + 10

• x + y = 100

  y = 3x + 20

• x + y = 100

  y = 2x + 20

Multiple Choice

What step is required first to solve this system by the substitution method?

x + y = 100

y = 3x + 20

• Subtract 3x from both sides of the equation

• Substitute y = 3x + 20 into x + y = 100

• Add x + y = 100 to y = 3x + 20

• Multiply by -3

Multiple Choice

What step is required first to solve this system by the elimination method?

x + y = 100

y = 3x + 20

• Subtract 3x from both sides of the equation

• Substitute y = 3x + 20 into x + y = 100

• Add x + y = 100 to y = 3x + 20

• Multiply by -3

Multiple Choice

Now that we've moved "3x"... What is the first step to solve this system by the elimination method?

x + y = 100

-3x + y = 20

• Multiply the first equation by -1 to eliminate "y"

• Multiply the second equation by -3 to eliminate "x"

• Add the first equation with the second.

• Multiply the first equation by 5 to eliminate "x"

Multiple Choice

Avery and Sophia went to the grocery store.  On Monday they purchased 4 apples and 6 bananas for a total of $13.  On Wednesday they purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4a + 6b = 3
  13.5a - 13b = 6

• a + b = 4
  a - b = 6

• 4x + 6y = 13
  3x + 7y = 13.5
• ax - 6a = 13
  bx - 7a = 13.5

Multiple Choice

George and Ruben went to the same grocery store on different days. George bought 5 squash and 2 zucchini for $7.32. Ruben bought 3 squash and 1 zucchini and his total $3.75.

Write a system of equations that models this scenario.

• 5q + 2z = 7.32
  1z = 3.75

• 5q + 2z = 7.32
  3q + 1z = 3.75

• 5q + z = 7.32
  3q + z = 3.75

• 5q + 2z = 7.75
  3q + 1z = 3.32

Multiple Choice

David mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins and it came to $6.60.  Which system of equations could be used to find the exact number of dimes and nickels? 

• d + n = 6.60
  .10d + .05n = 80
• .1d + .05n = 80
  .1d + .05n = 6.60

• d + n = 80
  .10d + .05n = 6.60
• d + n = 80
  .05d + .10n = 6.60

Multiple Choice

In Nyta's coin collection there are a total of 43 dimes and nickels. The coins are worth $3.05. How many of each type of coin are in the collection? Write a system of equations to model this scenario.

• x - y = 43

  25x + 10y = 3.05

• 25 dimes and 18 nickels
• x + y = 43

  .25x + .1y = 3.05

• .25x + .10y = 43

  25x + 10y = 3.05