System of Equations Problems

The most important step in solving system word problems is to ____________?

• Write the system

• Solve the system

• Define your variables

• Skip

Given the system
y = x² + 3x - 5
y = x + 3
Write the substitution equation (x² + 3x - 5 = x + 3) in standard form.

• x² + 4x - 2 = 0

• x² - 2x + 8 = 0

• x² + 2x - 8 = 0

• x² + 4x - 8 = 0

Given the system of equations: y = x² + 3x - 5 y = x + 3 When x = -4, what is the value of y?

• -1

• 1

• 7

• 0

Dennis 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

• d + n = 80
  d + n = 6.60

• d + n = 80
  .10d + .05n = 6.60

• d + n = 80
  .05d + .10n = 6.60

Some students want to order shirts with the WCHS school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

• y = 9.65 + x

  y = 8.40 + x

• y = 9.65x + 43

  y = 8.40x + 58

• y =9.65x

  y = 8.40x

• y = 9.65x - 43

  y = 8.40x - 58

What is the solution to the system of equations graphed below?

• No Solution

• Infinite Solutions

• One Solution: (3, 1)

• One Solution: (1, 3)

What is the solution to the system of equations graphed below?

• No Solution

• Infinite Solutions

• One Solution: (1, -2)

• One Solution: (-2, 1)

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, how old are Alex and Erin?

• x = 12

  y = 21

• x = 21

  y = 12

• x = 15

  y = 18

• x = 18

  y = 15

Nancy went to the grocery story. On Monday she purchased 12 oranges and 7 apples for a total of $5.36. On Wednesday she purchased 8 oranges and 5 apples for a total of $3.68. If x represents oranges and y represents apples, what did each orange and apple cost?

• x = $0.32

  y = $0 52

• x = $0.32

  y = $0.26

• x = $0.26

  y = $0.32

• x = $0.52

  y = $0.32

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)