Systems of Equations Strategy

The graph for the systems of linear equations y = 1/2x + 2 and y = x - 1 is shown below. This is a placeholder for the graph showing the systems of linear equations. What is the solution to the system of equations?

• (6, 5)

• (4, 0)

• (6, 4)

• (5, 6)

Krista and Tywana were solving the system of equations below. They each shared what strategy they would use to solve the system. Who do you agree with? Is either student wrong? This is a placeholder for the diagram showing the system of equations and the strategies proposed by Krista and Tywana.

• Krista is correct, because she used the substitution method.

• Tywana is correct, because she used the elimination method.

• Both Krista and Tywana are correct, because they used two different methods.

• Neither one of them is correct.

Solve the system of equations by using substitution. y = 2x + 3 y = x + 2 (x, y) = (_____, _____)

Parrish and Nadia's favorite store is having a sale. Parrish decides to purchase 3 new shirts and 3 pairs of pants for $120. Nadia purchases 2 new shirts and 3 pairs of pants for $105. This situation is modeled by the system of equations below, where s represents the cost of each shirt, and p represents the cost of each pair of pants. 3s + 3p = 120 2s + 3p = 105 How much does each shirt cost and each pair of pants cost?

• Each shirts costs $25 and each pair of pants costs $15

• Each shirts costs $15 and each pair of pants costs $25

• Each shirts costs $20 and each pair of pants cost $20

• Each shirts costs $20 and each pair of pants costs $15

Solve the system.

• (3, -2, 4)

• (2, -3, 1)

• (-3, 2, -1)

• Infinitely many solutions

Solve the system.

• (1, 2, -2)

• (1, -3, -2)

• (-1, 3, 2)

• No Solution

Solve the system. 

• (5, -6, 3)

• (2, 3, -1)

• (-4, 2, 5)

• No Solution

Solve the system.

• (2, -2, 3)

• (2, 1, 4)

• (-2, 2, -3)

• No Solution

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60