AnswersCMS 2026-2027 NC Math 1 CREDIT RECOVERYSystems of Equations and Inequalities

Systems of Equations and Inequalities — Test Answers

25 verified answers
1
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How many solutions does this linear system have? y is equal to 5 x minus 1 negative 15 x minus 3 y is equal to 3

A
one solution: 0 comma negative 1
B
one solution: 1 comma 4
C
infinite number of solutions
D
no solution
2
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Which statement describes the solution to the system of equations? 2 h plus 8 k is equal to 6 negative 5 h minus 20 k is equal to negative 15

A
The system has exactly one solution.
B
The system has infinitely many solutions.
C
The system has exactly two solutions.
D
The system has no solutions.
3

Which ordered pair (c,d) is the solution to the given system of linear equations? negative c plus 2 d is equal to 13 negative 9 c minus 4 d is equal to negative 15

A
open paren 6 comma negative 1 close paren
B
open paren 7 comma 10 close paren
C
open paren negative 1 comma 7 close paren
D
open paren negative 1 comma 6 close paren
4

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 plus y is equal to 24 3 x plus 5 y is equal to 100 What does the solution of this system indicate about the questions on the test?

A
The test contains 20 three-point questions and 8 five-point questions.
B
The test contains 4 three-point questions and 20 five-point questions.
C
The test contains 14 three-point questions and 10 five-point questions.
D
The test contains 10 three-point questions and 14 five-point questions.
5

Which statement correctly explains how Andre could find the solution to the following system of linear equations using elimination? 8 s minus 9 t is equal to 15 7 s minus 2 t is equal to 12

A
Multiply the first equation by 2 and the second equation by 9 , and then add.
B
Multiply the first equation by negative 7 and the second equation by 8 , and then add.
C
Multiply the first equation by negative 2 and the second equation by 9 , and then subtract.
D
Multiply the first equation by negative 7 and the second equation by 8 , and then subtract.
6

What is the solution to the system of equations? y is equal to negative 5 x plus 3 y is equal to 1

A
1 comma 0 point 4
B
1 comma 0 point 8
C
0 point 8 comma 1
D
0 point 4 comma 1
7

Which ordered pair open paren x comma y close paren is a solution to the given system of linear equations? 3 x plus y is equal to 1 5 x plus y is equal to 3

A
open paren 0 point 5 comma negative 0 point 5 close paren
B
open paren negative 2 comma 1 close paren
C
open paren 1 comma negative 2 close paren
D
open paren negative 0 point 5 comma 0 point 5 close paren
8

Which description of the graph of the linear inequality y is greater than or equal to 7 x minus 4 is correct?

A
The graph will be a solid line with a y -intercept of negative four and a slope of seven. The graph will be shaded above the line.
B
The graph will be a dashed line with a y -intercept of negative four and a slope of seven. The graph will be shaded below the line.
C
The graph will be a solid line with a y -intercept of seven and a slope of negative four. The graph will be shaded below the line.
D
The graph will be a dashed line with a y -intercept of seven and a slope of negative four. The graph will be shaded above the line.
9

Which ordered pair open paren A comma b close paren is the solution to the following system of equations? negative 2 A plus 3 b is equal to 14 A minus 4 b is equal to 3

A
open paren negative 4 comma negative 13 close paren
B
open paren 16 and 10 over 11 comma 8 over 11 close paren
C
open paren negative 13 comma negative 4 close paren
D
open paren negative 4 comma 13 close paren
10

The sum of two positive integers, a and b , is at least 30 The difference of the two integers is at least 10 If b is the greater integer, which system of inequalities could represent the values of a and b ?

A
a plus b is greater than or equal to 30 b is greater than or equal to a plus 10
B
a plus b is less than or equal to 30 b is less than or equal to a minus 10
C
a plus b is less than or equal to 30 b is greater than or equal to a plus 10
D
a plus b is greater than or equal to 30 b is less than or equal to a minus 10
11

What is the solution to the system of equations? 2⁢x+4⁢y=12 y=(1)/(4)⁢x−3

A
negative 1 comma 8
B
1 half comma 5
C
5 comma 1 half
D
8 comma negative 1
12

What is the solution to the system of equations?

A
7 comma 13 thirds
B
7 comma 4
C
8 comma 14 thirds
D
9 comma 7
13

Which value of m will create a system of parallel lines with no solution? y is equal to m x minus 6 8 x minus 4 y is equal to 12

A
2
B
negative 1 half
C
negative 2
D
1 half
14

What is the solution to the system of linear equations?

A
3 comma 1
B
negative 3 comma 3
C
0 comma 2
D
negative 3 comma 0
15

Which system is represented by the graph?

A
y is less than 2 x x plus 2 y is greater than or equal to negative 8
B
y is greater than 2 x x plus 2 y is less than or equal to negative 8
C
y is greater than or equal to 2 x x plus 2 y is less than negative 8
D
y is less than or equal to 2 x x plus 2 y is greater than negative 8
16

Which symbol could be written in both circles in order to represent this system algebraically? y circle 3 x x circle negative 2

A
is less than
B
is greater than
C
is less than or equal to
D
is greater than or equal to
17

Which statements must be true about their heights? Choose three correct answers.

A
Darius is at least 36 inches tall.
B
Darius is no more than 4 inches taller than twice William’s height.
C
William’s height is less than 68 inches.
D
Darius is less than 4 inches taller than twice William’s height.
E
William’s height is at least 68 inches.
F
Darius is at most 36 inches tall.
18

Which linear inequality is represented by the graph?

A
y is less than or equal to 1 third x minus 1 point 3
B
y is greater than or equal to 1 third x minus 1 point 3
C
y is greater than or equal to 1 third x minus 4 thirds
D
y is less than or equal to 1 third x minus 4 thirds
19

The solutions to the inequality y is greater than negative 3 x plus 2 are shaded on the graph. Which point is a solution?

A
1 comma negative 2
B
2 comma 0
C
0 comma 2
D
negative 2 comma 1
20

What is the solution to the system of equations?

A
0 comma negative 5
B
negative 5 comma 0
C
0 comma 5
D
5 comma 0

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