AnswersAISD Algebraic Reasoning B Credit Recovery 2026-2027Solving Systems of Linear Equations: Substitution

Solving Systems of Linear Equations: Substitution Answers

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

A
(–1.6, 1.6)
B
(–1.5, 1.5)
C
(1.5, –1.5)
D
(1.6, –1.6)
2
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The tables represent two linear functions in a system.What is the solution to this system?

Question illustration
A
(1, 0)
B
(1, 6)
C
(8, 26)
D
(8, –22)
3

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?y = 2x – 52y – 4x =

Question illustration
A
–10
B
–5
C
5
D
10
4

y=x – 6x=–4

Question illustration
A
(–8, –4)
B
(–4, –8)
C
(–4, 4)
D
(4, –4)
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?

A
One gym charges $75 per month.
B
Each gym charges $75 per month.
C
Both gyms charge the same monthly rate and the same membership fee.
D
Both gyms charge the same monthly rate, but not the same membership fee.
6

y=–5x + 30x=10

A
(–20, 10)
B
(10, –20)
C
(10, 4)
D
(4, 10)
7

y=–3x + 6y=9

A
(–21, 9)
B
(9, –21)
C
(–1, 9)
D
(9, –1)
8

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

A
(–40, 19)
B
(–19, 55)
C
(19, –40)
D
(55, –19)
9

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?

A
One landscaper charges $20 for 5 hours of work.
B
One landscaper’s hourly rate is $15 lower than the other landscaper’s.
C
Both landscapers charge the same hourly rate and the same fee per job.
D
Both landscapers charge the same hourly rate, but not the same fee per job.
10

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

Question illustration
A
(–8, 6)
B
(–6, 16)
C
(6, –8)
D
(16, –6)

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