question

What is the solution to the system of equations?
y= 1.5x - 4
y = -x

answer

(1.6, -1.6)

question

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?
y= 2x - 5
2y - 4x = []

answer

-10

question

Kathleen and Arnob both run from the park entrance along a loop. Kathleen starts walking from the park entrance and gets a 5-mile head start on Arnob. The graph shows how far they have both traveled.
How many minutes does it take Arnob to catch up to Kathleen?

answer

75

question

The tables represent two linear functions in a system.
What is the solution to this system?

answer

(8, -22)

question

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?

answer

The test contains 10 three-point questions and 14 five-point questions.

question

y = -5 + 30
x = 10
What is the solution to the system of equations?

answer

(10, -20)

question

Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below.
x - y = 7
3x - 2y = 8
Step 1: x = y + 7
Step 2: 3(y + 7) - 2y = 8
Step 3: 3y + 7 - 2y = 8
Step 4: y + 7 = 8
Step 5: y = 1
In which step did Ernesto make the first error?

answer

Step 3

question

y = 1/2x - 6
x = -4
What is the solution to the system of equations?

answer

(-4, -8)

question

What is the solution to the system of equations?
y= 2/3x + 3
x = -2

answer

(-2,5/3)

question

y = 4x - 10
y = 2
What is the solution to the system of equations?

answer

(3,2)

question

y = -3x + 6
y = 9
What is the solution to the system of equations?

answer

(-1, 9)

question

Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee.
Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75. What can Lian conclude?

answer

Both gyms charge the same monthly rate and the same membership fee.

question

What is the solution to the system of equations?
y= -3x - 2
5x + 2y = 15

answer

(-19, 55)

question

Which values, when placed in the box, would result in a system of equations with no solution? Check all that apply.
y = -2x + 4
6x + 3y = []

answer

-12
-4
0
4

question

Two linear equations are shown.
What is the solution to the system of equations?

answer

(7, 13/3)

question

What is the solution to the system of equations?
y= -5x + 3
y = 1

answer

(0.4, 1)

question

What is the solution to the system of equations?
y = -3x - 2
5x + 2y = 15

answer

(-19, 55)

question

Casey is deciding which of two landscapers to hire. Each landscaper charges an hourly rate plus a fee for each job.
Casey correctly wrote and solved a system of linear equations by substitution. In his work, he substituted an expression for one variable and solved for the other. This resulted in the equation 5 = 20. What can Casey conclude?

answer

Both landscapers charge the same hourly rate, but not the same fee per job.