Systems of Equations

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

Consider the system of equations: 6x + 2y = 4 6x + 6y = 24 What could be the first step in solving the system of equations using elimination?

• Multiply the second equation by 3

• Multiply the first equation by -1

• Add the two equations

• Add 4 to both sides of the first equation

Consider the system of equations below: -2x + 7y = 14 -2x + 7y = -7 How many solutions does the system of equations have?

• 2 solutions

• 1 solution

• No solution

• Infinitely Many Solutions

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)

What are the solutions to the systems of equations below? 3y = x - 2, y = -2x + 4

• (0, 2)

• (1, -2)

• (2, 0)

• (2, 4)

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.

If a system of equations had 2 lines that overlap, meaning they share all of the same points, how many solutions does the system have?

• One Solution

• Infinitely Many Solutions

• Two Solutions

• No Solution

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

Aiden uses a blend of dark chocolate and milk chocolate to make the ice cream topping at his restaurant. He needs to buy 100kg of chocolate in total for his next order. Dark chocolate costs $12 per kilogram, milk chocolate costs $10 per kilogram, and he wants to spend $1120 total. Let d be the number of kilograms of dark chocolate he buys and m be the number of kilograms of milk chocolate he buys. Which system of equations represents this situation?

• d + m = 100, 10d + 12m = 1120

• d + m = 1120, 12d + 10m = 100

• d + m = 100, 12d + 10m = 1120

• d + m = 1120, 10d + 12m = 100