System of Equations Questions

Which step below contains an error in

using substitution to solve the linear system 2x + y = 10

and 5y – 6x = 2?

• Step 1

• Step 2

• Step 3

• Step 4

Beth bought 15 tickets to a movie, where adult tickets cost $6.00 and senior citizen tickets cost $4.00. She spent a total of $76. Which two equations below represent the system of equations that could be used to determine the number of adult tickets, a, and the number of senior citizen tickets, s, Beth purchased?

• a + s = 76

• a + s = 15

• 4a + 6s = 15

• 6a + 4s = 76

• 4a + 6s = 76

Use elimination to solve the system above. What is the value of y?

• 1

• 5

• 3

• None of these

Sophie is trying to find two numbers, x and y, that satisfy the following conditions.

1. The sum of x and y is 35.

2. The sum of 2x and 2y is 70.

Sophie wrote the following system of equations to solve the problem.

x + y = 35

2x + 2y = 70

How many solutions does this system of equations have?

• 0

• 1

• 2

• Infinitely many solutions

The perimeter of a rectangular playground is 3,900 feet. The length of the playground is 40 feet greater than the width. Choose the two equations below that make up the system that can be used to determine l, the length, and w, the width of the playground?

• 2L + 2W = 3900

• L + W = 3900

• LW = 3900

• L + 40 = W

• W + 40 = L

Which of the following statements correctly describes the solution to the system of equations below?

x + y = 6

x - y = -14

• The two lines have slopes that are equal, and so the system has no solution.

• The two lines have slopes that are equal, and so the system has one solution.

• The two lines have slopes that are different, and so the system has no solution.

• The two lines have slopes that are different, and so the system has one solution.

A system of equations is represented by the table shown. What is the solution to the system of equations?

• (-1, 5)

• (1, 7)

• (0, 3)

• No solution

Use a coordinate plane to create a graph representing a system of linear equations. Line 1 is represented by the equation in point-slope form, y-5 = -0.5(x+8); line 2 passes through (-8, -7) and (-4, -6). What is the solution to the system of equations?

• (8, -3)

• (6, -2)

• (8, -2)

• (5, -1)

Use substitution to solve the system below. What is the x-coordinate?

x = 3y + 3

y + 3x = -21

• -4.2

• -5.1

• -6

• -3

A zookeeper needs to mix feed for the prairie dogs so that the feed has the right amount of protein. Feed A has 12% protein. Feed B has 5% protein. Choose the two equations that would represent the system of equations that could be used to determine the amount of each feed he would need to mix to get 100 lb of feed that is 8% protein?

Let A represent the amount of feed A in the mixture; let B represent the amount of feed B in the mixture.

• A + B = 100

• 0.12 A + 0.05B = 100

• 0.12A + 0.05B = 0.08(100)

• A + B = 0.08(100)