AnswersAlgebra ISystems of Equations and Inequalities

Systems of Equations and Inequalities — Test Answers

25 verified answers
1
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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 less than or equal to 1 third x minus 4 thirds
C
y is greater than or equal to 1 third x minus 4 thirds
D
y is greater than or equal to 1 third x minus 1 point 3
2
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How many paperback books did Gillian buy?

A
12
B
14
C
13
D
11
3

Which system of linear inequalities is represented by the graph?

A
y is greater than or equal to x plus 2 and x plus 2 y is less than 4
B
y is greater than or equal to x minus 2 and x plus 2 y is less than 4
C
y is greater than x minus 2 and x plus 2 y is less than negative 4
D
y is greater than or equal to x minus 2 and x minus 2 y is less than 4
4

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
negative 2 comma 1
D
0 comma 2
5

What is the solution to this system of linear equations? 7 x minus 2 y is equal to negative 6; 8 x plus y is equal to 3

A
1 comma negative 5
B
0 comma 3
C
15 comma negative 1
D
negative 6 comma 3
6

What is the solution to this system of linear equations? 3 x minus 2 y is equal to 14; 5 x plus y is equal to 32

A
6 comma 2
B
14 comma negative 18
C
8 comma negative 1
D
3 comma 5
7

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 A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A dashed line with a negative slope passes through approximately the points 0 comma 2, 2 comma 1, and 4 comma 0. The region above the dashed line is shaded.
B
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A solid line with a negative slope passes through approximately the points 0 comma 2, 2 comma 1, and 4 comma 0. The region below the solid line is shaded.
C
Image with description A coordinate plane with a straight line of negative slope and a shaded region. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The line extends from the upper-left area of the plane near negative 4 comma 4 to the lower-right area near 4 comma 1, passing through the upper-center portion of the plane. The region above the line is shaded.
D
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A dashed line with a negative slope passes through approximately the points 0 comma 2, 2 comma 1, and 4 comma 0. The region below the dashed line is shaded.
8

What is the value of y in the solution to the system of equations? 1 third x plus 1 fourth y is equal to 1 2 x minus 3 y is equal to negative 30

A
3
B
negative 3
C
negative 8
D
8
9

The system of equations can be solved using linear combination to eliminate one of the variables. 2 x minus y equals negative 4 right arrow 10 x minus 5 y equals negative 20; 3 x plus 5 y = 59 right arrow 3 x plus 5 y equals 59; 13 x equals 39 Which equation can replace 3 x plus 5 y is equal to 59 in the original system and still produce the same solution?

A
13 x is equal to 39
B
2 x minus y is equal to negative 4
C
7 x is equal to 39
D
10 x minus 5 y is equal to negative 20
10

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 8 comma 1
B
0 point 4 comma 1
C
1 comma 0 point 4
D
1 comma 0 point 8
11

At an end of the year sale, Gabriela bought more than 12 bottles of hand soaps and lotions. If x represents the number of hand soaps and y represents the number of lotions she bought, which inequality best represents her purchase?

A
x plus y is less than or equal to 12
B
x plus y is greater than or equal to 12
C
x plus y is less than 12
D
x plus y is greater than 12
12

A snack tray at a party has cheese squares with 2 grams of protein apiece and turkey slices with 3 grams of protein apiece. Which inequality represents the possible ways Nina can eat 12 or more grams of protein, if x is the number of cheese squares that she eats and y is the number of turkey slices that she eats?

A
12 is less than or equal to 2 x plus 3 y
B
12 is less than or equal to x plus y
C
12 is greater than or equal to x plus y
D
12 is greater than or equal to 2 x plus 3 y
13

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

What is the solution to the system of equations?

A
9 comma 7
B
7 comma 13 thirds
C
7 comma 4
D
8 comma 14 thirds
15

Which inequality pairs with y is less than or equal to negative 2 x minus 1 to complete the system of linear inequalities represented by the graph?

A
y is less than negative 2 x plus 2
B
y is less than 2 x minus 2
C
y is greater than or equal to negative 2 x plus 2
D
y is greater than 2 x minus 2
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 greater than
B
is less than
C
is less than or equal to
D
is greater than or equal to
17

Which linear inequality is represented by the graph?

A
y is greater than 2 thirds x plus 3
B
y is less than 2 thirds x plus 3
C
y is greater than 3 halves x plus 3
D
y is less than 3 halves x plus 3
18

Which combination of loaves of bread and batches of muffins could Helena bake?

A
2 loaves of bread and 4 batches of muffins
B
5 loaves of bread and 1 batch of muffins
C
3 loaves of bread and 3 batches of muffins
D
4 loaves of bread and 2 batches of muffins
19

What is the maximum length possible for her blanket?

A
90 inches
B
45 inches
C
60 inches
D
30 inches
20

What is the solution to the system of equations?

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

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