AnswersAISD Algebraic Reasoning B Credit Recovery 2026-2027Unit Test

Unit Test — Unit test Answers

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What is the solution to this system of linear equations?x + y = 4x − y = 6

A
(4, 6)
B
(6, 4)
C
(5, −1)
D
(−1, 5)
2
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The graph below represents the system of equations 3x+4y=12 and 2x-y=8.

Question illustration
A
(0, 3)
B
(3, 0)
C
(4, 0)
D
(0, 4)
3

The system of equations can be solved using linear combination to eliminate one of the variables.2x − y = −4→10x − 5y = −203x + 5y = 59→3x + 5y = 59 13x = 39Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?

A
2x – y = –4
B
10x – 5y = –20
C
7x = 39
D
13x = 39
4

Erik rode down an escalator, while Raj rode up.

Question illustration
A
Erik and Raj were at the same elevation after both of them had been riding the escalator for 6 seconds.
B
Erik and Raj were at the same elevation after both of them had been riding the escalator for 8 seconds.
C
Erik and Raj were at the same elevation after Erik had been riding the escalator for 6 seconds and Raj had been on the escalator for 8 seconds.
D
Erik and Raj were at the same elevation after Erik had been riding the escalator for 8 seconds and Raj had been on the escalator for 6 seconds.
5

y=5x – 1–15x – 3y=3

A
one solution: (0, –1)
B
one solution: (1, 4)
C
no solution
D
infinite number of solutions
6

Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. Helena has 17 cups of flour and 4.5 cups of sugar available for baking.

A
2 loaves of bread and 4 batches of muffins
B
3 loaves of bread and 3 batches of muffins
C
4 loaves of bread and 2 batches of muffins
D
5 loaves of bread and 1 batch of muffins
7

Which value of m will create a system of parallel lines with no solution?y=mx-68x-4y=12

Question illustration
A
-2
B
-
Option B
C
Option
Option C
D
2
8

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.x + y = 243x + 5y = 100What does the solution of this system indicate about the questions on the test?

A
The test contains 4 three-point questions and 20 five-point questions.
B
The test contains 10 three-point questions and 14 five-point questions.
C
The test contains 14 three-point questions and 10 five-point questions.
D
The test contains 20 three-point questions and 8 five-point questions.
9

To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?First equation: 4x − 3y = 34Second equation: 3x + 2y = 17

A
The first equation should be multiplied by 2 and the second equation by 3.
B
The first equation should be multiplied by 2 and the second equation by −3.
C
The first equation should be multiplied by 3 and the second equation by 4.
D
The first equation should be multiplied by 3 and the second equation by −4.
10

What is the solution to the system of equations?y = –5x + 3y = 1

A
(0.4, 1)
B
(0.8, 1)
C
(1, 0.4)
D
(1, 0.8)
11

Two linear equations are shown.

Question illustration
A
(7, 4)
B
(7, StartFraction 13 over 3 EndFraction)
Option B
C
(8, StartFraction 14 over 3 EndFraction)
Option C
D
(9, 7)
12

A coordinate grid with 2 lines. The first line is labeled y equals 0.5 x plus 3.5 and passes through (negative 3, 1), (negative 2.7, 2.1), and (0, 3.5). The second line is labeled y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction and passes through the points (negative 4, 3), (negative 2.7, 2.1), and (StartFraction 1 over 3 EndFraction, 0).

Question illustration
A
(–2.7, 2.1)
B
(–2.1, 2.7)
C
(2.1, 2.7)
D
(2.7, 2.1)
13

A coordinate grid with 2 lines. The first line passes through (0, negative 5) and (negative 5, 0). The second line passes through (0, negative 5) and (negative 2, 1).

Question illustration
A
(5, 0)
B
(0, 5)
C
(0, –5)
D
(–5, 0)
14

Jamie and Owen joined a monthly walking challenge at their youth center. Jamie has already walked 120 minutes and plans to walk 20 minutes per day. Owen plans to walk 30 minutes per day. Let x represent the number of days and y represent the total number of minutes walked during the challenge. Which system of equations can be used to find the number of days it will take for Owen and Jamie to have walked the same number of minutes?

A
A system of equations. y equals 20 x plus 120. y equals 30 x.
Option A
B
A system of equations. y equals 20 x. y equals 30 x plus 120.
Option B
C
A system of equations. y equals 120 x plus 20. y equals 30 x.
Option C
D
A system of equations. y equals 120 x. y equals 30 x plus 20.
Option D
15

What is the value of y in the solution to the system of equations?x + y = 12x – 3y = –30

Question illustration
A
–8
B
–3
C
3
D
8
16

What is the solution to this system of linear equations?3x – 2y = 14 5x + y = 32

A
(3, 5)
B
(6, 2)
C
(8, –1)
D
(14, –18)
17

Gillian purchased 25 books at the library book sale. Each hardcover book cost $1.50, and each paperback book cost $0.50. Gillian spent a total of $26.50. The book costs can be represented by the system of equations below. h + p = 251.50h + 0.50p = 26.50

A
11
B
12
C
13
D
14
18

The graph represents this system of equations.

Question illustration
A
(–4, 1)
B
(–2, 1)
C
(1, –4)
D
(1, –2)
19

What is the solution to this system of linear equations?7x – 2y = –68x + y = 3

A
(–6, 3)
B
(0, 3)
C
(1, –5)
D
(15, –1)
20

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

Question illustration
A
-12
B
-4
C
4
D
12

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