Answers Algebra ISolving Systems of Linear Equations: Graphing

Solving Systems of Linear Equations: Substitution Answers

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

(1, 0)

(1, 6)

(8, 26)

(8, –22)

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What is the solution to the system of equations?y = x – 102x + y = 4

(–8, 6)

(–6, 16)

(6, –8)

(16, –6)

y=–3x + 6y=9

(–21, 9)

(9, –21)

(–1, 9)

(9, –1)

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

(negative 2, negative StartFraction 15 over 2 EndFraction)

(negative 2, StartFraction 5 over 3 EndFraction)

(negative 2, StartFraction 11 over 6 EndFraction)

(negative 2, StartFraction 13 over 3 EndFraction)

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

Step 1

Step 2

Step 3

Step 4

What is the solution to the system of equations?y = –3x – 25x + 2y = 15

(–40, 19)

(–19, 55)

(19, –40)

(55, –19)

y=–5x + 30x=10

(–20, 10)

(10, –20)

(10, 4)

(4, 10)

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?

One gym charges $75 per month.

Each gym charges $75 per month.

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

Both gyms charge the same monthly rate, but not the same membership fee.

y=4x – 10y=2

(3, 2)

(2, 3)

(–2, 2)

(2, –2)

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

(negative StartFraction 13 over 3 EndFraction, negative 25)

(negative StartFraction 14 over 3 EndFraction, negative 54)

(–13, –50)

(–14, –54)

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

(–1.6, 1.6)

(–1.5, 1.5)

(1.5, –1.5)

(1.6, –1.6)

y=x – 6x=–4

(–8, –4)

(–4, –8)

(–4, 4)

(4, –4)

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?

One landscaper charges $20 for 5 hours of work.

One landscaper’s hourly rate is $15 lower than the other landscaper’s.

Both landscapers charge the same hourly rate and the same fee per job.

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

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.

9.8

73.5

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Solving Systems of Linear Equations: Substitution Answers

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