Solving Systems of Linear Equations: Substitution (6.2.2)

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

-10

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

(10, -20)

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

(-19, 55)

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

(-19, 55)

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?

Step 3

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

(3,2)

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

(1.6, -1.6)

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?

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

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

(-4, -8)

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

(0.4, 1)

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

(7, 13/3)

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

(-2,5/3)

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 = []

-12 -4 0 4

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?

75

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?

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

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

(-1, 9)

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

(8, -22)

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?

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