System of Linear Equations M2T3 Practice

Solve the system of equations by substitution.

y = 2x - 3

x = 4

Solve the system of equations by substitution.

2x + y = 9

y = 5x + 2

Solve the system of equations by substitution. Determine whether the system is consistent or inconsistent.

y = 3x - 2

y - 3x = 4

• (3,2), consistent

• No Solution, inconsistent

• (-3,-2), consistent

• (3,4), consistent

Write a system of equations to represent the following problem situation. Solve the system of equations using any method. Rachel needs to print some of her digital photos. She is trying to choose between Lightning Fast Foto and Snappy Shots. Lightning Fast Foto charges a base fee of $5 plus an additional $0.20 per photo. Snappy Shots charges a base fee of $7 plus an additional $0.10 per photo. Determine the number of photos for which both stores will charge the same amount.

• y=0.20x+5, y=0.10x+7, (20,9)

• y=0.20x+7, y=0.10x+5, (20,9)

• y=0.20x+5, y=0.10x+7, (9,20)

• y=0.20x+7, y=0.10x+5, (9,20)

Write a system of equations to represent the following problem situation. Solve the system of equations using any method.

Raja is trying to decide which ice cream shop is the better buy. Cold & Creamy Sundaes charges $2.50 per sundae plus an additional $0.25 for each topping. Colder & Creamier Sundaes charges $1.50 per sundae plus an additional $0.50 for each topping. Determine the number of toppings for which both vendors charge the same amount.

Write a system of equations to represent the following problem situation. Solve the system of equations using any method.

Alicia has a booth at the flea market where she sells purses and wallets. All of her purses are the same price and all of her wallets are the same price. The first hour of the day, she sells 10 purses and 6 wallets for a total of $193. The second hour, she sells 2 purses and 1 wallet for a total of $37.50. How much does Alicia charge for each purse and each wallet?

Write a system of equations to represent the following problem situation. Solve the system of equations using any method.

Ms. Williamson woke up one morning to find that her water heater had sprung a leak. She called two different plumbers to get their rates. The first plumber charges sixty-four dollars just to walk in the door plus twenty-four dollars an hour. The second plumber charges a flat fifty-six dollars an hour. After how many hours will the cost for both plumbers be the same?

Solve the system of equations. -8x - 8y = -10 x = 3.25

• 3.25,-2

• -2,3.25

• -3.25,-2

• -3.25,2

Solve the system of equations and plot the solution on the graph. -1.5x + 0.5y = -2 y + 7 = 3(x + 1)

• One Solution

• No Solution

• Infinite Solution

• Two Solutions

Solve the system of equations using the linear combinations method: 3x + 5y = 8 2x - 5y = 22