Question 1

Use the method of substitution to solve the system.

Accepted Answer

The answer of Use the method of substitution to solve...

Question 2

A small firm manufactures bookshelves and desks for microcomputers. For each product it is necessary to use a table saw and a power router. To manufacture each bookshelf, the saw must be used for  hour and the router for 1 hour. A desk requires the use of each machine for 2 hours. The profits are $20 per bookshelf and $50 per desk. If the saw can be used for 8 hours per day and the router for 12 hours per day, how many bookshelves and desks should be manufactured each day to maximize the profit?

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Question 3

Use Cramer's rule, whenever possible, to solve the system.

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Question 4

Use matrices to solve the system.

Accepted Answer

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...

Question 5

Find the inverse of the matrix if it exists.

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Question 6

Solve the system  using the inverse method.

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Question 7

A stationary company makes two types of notebooks: a deluxe notebook with subject dividers, which sells for $1.25, and a regular notebook, which sells for $0.9. The production cost is $1.00 for each deluxe notebook and $0.75 for each regular notebook. The company has the facilities to manufacture between 2,000 and 3,000 deluxe and between 3,000 and 6,000 regular notebooks, but not more than 8,000 altogether. How many notebooks of each type should be manufactured to maximize the difference between the selling prices and the production cost?

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Question 8

Find the determinant of the matrix.

Accepted Answer

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...

Question 9

Use the method of substitution to solve the system.

Accepted Answer

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Question 10

Find the determinant.

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...

Question 11

A manufacturer of cell phones makes a profit of $26 on a deluxe model and $30 on a standard model. The company wishes to produce at least 80 deluxe models and at least 100 standard models per day. To maintain high quality, the daily production should not exceed 240 phones. How many of each type should be produced daily in order to maximize the profit?

Accepted Answer

To maximize profit, the company should produce as many of the higher profit standard models as possible while meeting the constraints. Producing 160 standard and 80 deluxe models maximizes profit while staying within the production limits.

Question 12

Let  be the identity matrix of order 2, and let  . Find the polynomial  for the given matrix A. (In the study of matrices,  is the characteristic polynomial of A, and the zeros of  are the characteristic values (eigenvalues) of A.)

Accepted Answer

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Question 13

Use matrices to solve the system.

Accepted Answer

The answer of Use matrices to solve the system. 
...

Question 14

Find a system of inequalities for the graph shown.

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Question 15

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.

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Question 16

Solve the system.

Accepted Answer

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...

Question 17

Find the inverse of the matrix if it exists.

Accepted Answer

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Question 18

Use the method of substitution to solve the system.

Accepted Answer

The answer of Use the method of substitution to solve...

Question 19

Use the method of substitution to solve the system.

Accepted Answer

The answer of Use the method of substitution to solve...

Question 20

Find the inverse of the matrix if it exists.

Accepted Answer

The answer of Find the inverse of the matrix if...

Quiz 9: Systems of Equations and Inequalities

Use the method of substitution to solve the system.

Use Cramer's rule, whenever possible, to solve the system.

Use matrices to solve the system.

Find the inverse of the matrix if it exists.

Solve the system using the inverse method.

Find the determinant of the matrix.

Use the method of substitution to solve the system.

Find the determinant.

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A. (In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)

Use matrices to solve the system.

Find a system of inequalities for the graph shown.

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.

Solve the system.

Find the inverse of the matrix if it exists.

Use the method of substitution to solve the system.

Use the method of substitution to solve the system.

Find the inverse of the matrix if it exists.