Grade 8 Solving Systems of Linear Equations

Looking at the graphs below, which graph has a solution of (0,4)?

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Model the following systems of equations:

y = 2x + 4

y = 2x + 1

The diagram above shows the graphs of these equations. Which statement best describes the system?

• The system is inconsistent and has no solution.

• The system is consistent and has no solution.

• The system is inconsistent and has one solution.

• The system is consistent and has infinitely many solutions.

In which system are the lines parallel?

• 2x - y = 3

  x + 2y = 3

• 2x + 3y = 5

  6x + 9y = 1

• x - y = 10

  x + y = 10

• 3x - y = 1

  4x + y = 2

Which system of equations best describes the lines in the graph?

Avery was selling concessions at the basketball game. She is selling pizza by the slice for $3.50 and sports drinks for $2.00. She sold a total of 96 slices of pizza and sports drinks combined. Avery made a total of $300. If x represents a slice of pizza and y represents a sports drink, which system of equations best describes this situation?

• 2x + 3.5y = 300

  x + y = 96

• 3.5x + 2y = 300

  x + y = 96

• 2x + 3.5y = 96

  x + y = 300

• 3.5x + 2y = 96

  x + y = 300

Avery was selling concessions at the basketball game. She is selling pizza by the slice for $3.50 and sports drinks for $2.00. She sold a total of 96 slices of pizza and sports drinks combined. Avery made a total of $300. If x represents a slice of pizza and y represents a sports drink, how many slices of pizza and sports drinks did she sell?

• 55 slices of pizza

  41 sports drinks

• 41 slices of pizza

  55 sports drinks

• 72 slices of pizza

  24 sports drinks

• 24 slices of pizza

  72 sports drinks

How long can someone skate at both places and the price is the same?

• 0.25 hours

• 2.5 hours

• 4 hours

• 10 hours

The farmers market sells strawberries and pineapples in a fruit basket. If s represents strawberries and p represents pineapples, which system of equations represents the cost of each fruit basket?

• 7s + 2p = 28

  3s + 2p = 20

• 7s + 2p = 20

  3s + 2p = 28

• 7s + 3p = 28

  2s + 2p = 20

• 2s + 7p = 28

  2s + 3p = 20

The farmers market sells strawberries and pineapples in a fruit basket. What is the cost of each fruit?

• Strawberries: $3 Pineapples: $5

• Strawberries: $5 Pineapples: $3

• Strawberries: $2 Pineapples: $7

• Strawberries: $7

  Pineapples: $2

Find the line that contains the error when using substitution to solve a system of equations.

• Line 1

• Line 2

• Line 3

• Line 4