Solving Systems of Linear Equations: Substitution

Question 1

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?

Revolt · Accepted Answer

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

Question 2

Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below.x – y = 73x – 2y = 8Step 1: x = y + 7Step 2: 3(y + 7) – 2y = 8Step 3: 3y + 7 – 2y = 8Step 4: y + 7 = 8Step 5: y = 1

Revolt · Accepted Answer

Step 3

Question 3

y=–3x + 6y=9

Revolt · Accepted Answer

(–1, 9)

Question 4

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

Revolt · Accepted Answer

(negative 2, StartFraction 5 over 3 EndFraction)

Question 5

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?

Revolt · Accepted Answer

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

Question 6

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

Revolt · Accepted Answer

(8, –22)

Question 7

y=x – 6x=–4

Question 8

y=–5x + 30x=10

Revolt · Accepted Answer

(10, –20)

Question 9

y=4x – 10y=2

Revolt · Accepted Answer

(3, 2)

Question 10

y=x – 6x=–4

Revolt · Accepted Answer

(–4, –8)

Solving Systems of Linear Equations: Substitution Answers

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