Answers FL-1200310-Algebra 1Solving Systems of Linear Equations: Substitution

Solving Systems of Linear Equations: Substitution Answers

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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

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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)

The soccer team is planning to sell health bars for a fundraiser. The prices of purchasing health bars from two different companies are represented by the system of equations shown, where x is the number of bars purchased and y is the total cost in dollars.Company A: y=0.75xCompany B: y=10+0.50x

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

(1, 0)

(1, 6)

(8, 26)

(8, –22)

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?y = -2x + 46x + 3y =

-12

-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.

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