Question 1

Solve the system of inequalities by graphing the solution region.

Accepted Answer

The solution region is the shaded area above the line y > -x + 3 and below the line y < -x + 5. These lines intersect at (-1,4) and form a diagonal boundary for the shaded region. All points above the top line and below the bottom line satisfy both inequalities, so the shaded region is the solution to the system of inequalities.

Question 2

Determine the size of the matrix and identify the entry located in the second row and first column.

Accepted Answer

The answer of Determine the size of the matrix and...

Question 3

Solve the system of inequalities by graphing the solution region.

Accepted Answer

The answer of Solve the system of inequalities by graphing...

Question 4

Solve the system of inequalities by graphing the solution region.

Accepted Answer

The answer of Solve the system of inequalities by graphing...

Question 5

Write the system of equations for the matrix. Then use back-substitution to find its solution.

Accepted Answer

The answer of Write the system of equations for the...

Question 6

Determine whether the ordered pairs given are solutions to the system.  (0, 0), (3, -1), (-3, -3), and (-5, 1)

Accepted Answer

The answer of Determine whether the ordered pairs given are...

Question 7

Solve the system of inequalities by graphing the solution region.

Accepted Answer

In option D, the shaded area is the only region common to both inequalities. The lines y = x and y = -x + 4 intersect at the point (2, 2), which is reflected in the graph. The region above the line y = x satisfies the inequality y > x, and the region below the line y = -x + 4 satisfies the inequality y < -x + 4. Thus, the shaded region represents the solution to the system of inequalities.

Question 8

Determine the size of the matrix and identify the entry located in the second row and first column.

Accepted Answer

The notation F1F1F1S1F1F1F10 represents a matrix with 3 rows and 10 columns where the entries are real numbers. So the size of the matrix is 2 F1F1F1S1F1F1F10. 
To identify the entry located in the second row and first column, we look for the element in the second row (since the matrix has two rows) and first column (since the matrix has 10 columns) which is 3; 6. So the answer is choice B.

Question 9

Solve the system of inequalities by graphing the solution region.

Accepted Answer

The answer of Solve the system of inequalities by graphing...

Question 10

Perform the indicated row operation, then write the new matrix.  -2R1 + R2 → R2

Accepted Answer

The answer of Perform the indicated row operation, then write...

Question 11

Use the following to answer questions : 
-Use back-substitution to find the solution.

Accepted Answer

The correct solution is (27, -7, -5) because back-substitution typically involves solving equations from the bottom up in a system of linear equations, ensuring that each variable satisfies its respective equation. This choice correctly reflects the values of the variables that would result from such a process.

Question 12

Form the augmented matrix, then name the diagonal entries of the coefficient matrix.

Accepted Answer

The answer of Form the augmented matrix, then name the...

Question 13

Solve the system of inequalities by graphing the solution region.

Accepted Answer

The answer of Solve the system of inequalities by graphing...

Question 14

Solve the system of inequalities by graphing the solution region.

Accepted Answer

The answer of Solve the system of inequalities by graphing...

Question 15

A stationary store sells rolls of standard gift wrap and deluxe gift wrap. They can stock a total of 110 rolls of gift wrap, of which at least 40 must be standard wrap and at least 20 must be deluxe wrap. The profit on a roll of standard wrap is $4 and the profit on a roll of deluxe wrap is $5. How many rolls of each type of gift wrap should the store stock to maximize their profit?

Accepted Answer

The answer of A stationary store sells rolls of standard...

Question 16

Use the following to answer questions :
Esther wants to spend no more than $60 buying gifts for her friends Barb and Wanda. She wants to spend at least $20 on Wanda's gift.
-Solve the system of linear inequalities.

Accepted Answer

Let x be the amount of money Esther spends on Barb's gift. Then, the system of linear inequalities is:
x + y ≤ 60 (Esther wants to spend no more than $60 in total)
y ≥ 20 (Esther wants to spend at least $20 on Wanda's gift)
where y represents the amount of money Esther spends on Wanda's gift. To graph this system, we first graph the boundary lines: x + y = 60 and y = 20. The region that satisfies both inequalities is the shaded region above the line y = 20 and below the line x + y = 60. Since Esther wants to spend as little as possible on Barb's gift, she should choose the point on the line x + y = 60 that is closest to the y-axis. This point is (0, 60), which means she should spend $0 on Barb's gift and $60 on Wanda's gift. Therefore, the best choice is B.

Question 17

Use the following to answer questions : 
-Write the system of equations corresponding to the matrix.

Accepted Answer

The answer of Use the following to answer questions :...

Question 18

Use the following to answer questions :
Esther wants to spend no more than $60 buying gifts for her friends Barb and Wanda. She wants to spend at least $20 on Wanda's gift.
-Let B represent the amount Esther spends on Barb's gift and W represent the amount she spends on Wanda's gift. Write a system of linear inequalities that models the information.

Accepted Answer

The answer of Use the following to answer questions :
Esther...

Question 19

Determine which of the ordered pairs given produces the maximum value of P(x, y). P(x, y) = 20x + 50y; (0, 0), (5, 2), (4, 0), (0, 6)

Accepted Answer

P(0, 6) = 20(0) + 50(6) = 300, which is the maximum value of P(x, y).

Question 20

Form the augmented matrix, then name the diagonal entries of the coefficient matrix.

Accepted Answer

The answer of Form the augmented matrix, then name the...

Quiz 8: Systems of Equations and Inequalities

Solve the system of inequalities by graphing the solution region.

Determine the size of the matrix and identify the entry located in the second row and first column.

Solve the system of inequalities by graphing the solution region.

Solve the system of inequalities by graphing the solution region.

Write the system of equations for the matrix. Then use back-substitution to find its solution.

Determine whether the ordered pairs given are solutions to the system. (0, 0), (3, -1), (-3, -3), and (-5, 1)

Solve the system of inequalities by graphing the solution region.

Determine the size of the matrix and identify the entry located in the second row and first column.

Solve the system of inequalities by graphing the solution region.

Perform the indicated row operation, then write the new matrix. -2R1 + R2 → R2

Use the following to answer questions : -Use back-substitution to find the solution.

Form the augmented matrix, then name the diagonal entries of the coefficient matrix.

Solve the system of inequalities by graphing the solution region.

Solve the system of inequalities by graphing the solution region.

Use the following to answer questions : Esther wants to spend no more than $60 buying gifts for her friends Barb and Wanda. She wants to spend at least $20 on Wanda's gift. -Solve the system of linear inequalities.

Use the following to answer questions : -Write the system of equations corresponding to the matrix.

Determine which of the ordered pairs given produces the maximum value of P(x, y) . P(x, y) = 20x + 50y; (0, 0) , (5, 2) , (4, 0) , (0, 6)

Form the augmented matrix, then name the diagonal entries of the coefficient matrix.