AnswersTX-Algebra I A-CRUnit Test

Solving Systems: Introduction to Linear Combinations Answers

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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.
2
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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)
3

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)
4

y=4x – 10y=2

A
(3, 2)
B
(2, 3)
C
(–2, 2)
D
(2, –2)
5

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

Question illustration
A
(negative StartFraction 13 over 3 EndFraction, negative 25)
Option A
B
(negative StartFraction 14 over 3 EndFraction, negative 54)
Option B
C
(–13, –50)
D
(–14, –54)
6

y=x – 6x=–4

Question illustration
A
(–8, –4)
B
(–4, –8)
C
(–4, 4)
D
(4, –4)
7

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

Question illustration
A
(negative 2, negative StartFraction 15 over 2 EndFraction)
Option A
B
(negative 2, StartFraction 5 over 3 EndFraction)
Option B
C
(negative 2, StartFraction 11 over 6 EndFraction)
Option C
D
(negative 2, StartFraction 13 over 3 EndFraction)
Option D
8

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

A
Step 1
B
Step 2
C
Step 3
D
Step 4
9

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
10

y=–5x + 30x=10

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

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