AnswersAlgebra 1Systems of Equations and Inequalities

Systems of Equations and Inequalities — Test Answers

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A wholesaler requires a minimum of 4 items in each order from its retail customers. The manager of one retail store is considering ordering a certain number of sofas, x , and a certain number of pillows that come in pairs, y Which graph represents the overall equation represented by this scenario? (All points may not apply to the scenario.)

A
Image with description On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.
B
Image with description On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2) and (4, 0). Everything above and to the right of the line is shaded.
C
Image with description On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything above and to the right of the line is shaded.
D
Image with description On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.
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 4 three-point questions and 20 five-point questions.
B
The test contains 14 three-point questions and 10 five-point questions.
C
The test contains 20 three-point questions and 8 five-point questions.
D
The test contains 10 three-point questions and 14 five-point questions.
5

A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point. If x is the number of solved puzzles and y is the number of solved riddles, which graph represents the overall equation represented by this scenario? (All points may not apply to the scenario.)

A
Image with description On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below the line is shaded.
B
Image with description On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the right of the line is shaded.
C
Image with description On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything above the line is shaded.
D
Image with description On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the left of the line is shaded.
7

Anatoliy has a combination of 104 nickels and quarters totaling 22 dollars Which system of linear equations can be used to find the number of nickels, n , and the number of quarters, q , Anatoliy has?

A
n plus q is equal to 104 0 point 0 5 n plus 0 point 2 5 q is equal to 22
B
n plus q is equal to 104 5 n plus 25 q is equal to 22
C
n is equal to q is equal to 22 0 point 0 5 n plus 0 point 2 5 q is equal to 104
D
n plus q is equal to 22 5 n plus 25 q is equal to 104
9

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 less 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 greater than or equal to 30 b is less than or equal to a minus 10
D
a plus b is greater than or equal to 30 b is greater than or equal to a plus 10
10

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 dashed line with a y -intercept of negative four and a slope of seven. The graph will be shaded below the line.
B
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.
C
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.
D
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.
12

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

A
0 point 4 comma 1
B
0 point 8 comma 1
C
1 comma 0 point 4
D
1 comma 0 point 8
13

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
8 comma negative 1
C
1 half comma 5
D
5 comma 1 half
14

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
15

Which is the approximate solution to the system y is equal to 0 point 5 x plus 3 point 5 and y is equal to negative 2 thirds x plus 1 third shown on the graph?

A
2 point 7 comma 2 point 1
B
2 point 1 comma 2 point 7
C
negative 2 point 1 comma 2 point 7
D
negative 2 point 7 comma 2 point 1
17

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
18

What is the solution to the system of linear equations?

A
negative 3 comma 0
B
3 comma 1
C
negative 3 comma 3
D
0 comma 2
19

Which linear inequality is represented by the graph?

A
y is less than 2 thirds x plus 3
B
y is greater than 2 thirds x plus 3
C
y is less than 3 halves x plus 3
D
y is greater than 3 halves x plus 3
20

What is the solution to the system of equations?

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

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