Exam 8: Systems of Equations and Inequalities

Solve the system by elimination. The system must first be written in standard form.

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?

Solve the system of equations using Cramer's rule, if possible. Do not use a calculator.

Solve the system of inequalities by graphing the solution region.

Perform the indicated operation, if possible. Do not use a calculator. If the operation cannot be completed, state why. A + B

Determine if the ordered triple (2, -1, 1) is a solution of the system.

Solve using any method and identify the system as consistent, inconsistent, or dependent.

Write the determinants D, D_x, and D_y for the system. Do not solve.

Solve the system by elimination.

Solve the system by triangularizing the augmented matrix and using back substitution. If the system is linearly dependent, give the solution in terms of a parameter.

Determine if the ordered triple (0, -2, 1) is a solution of the system.

Solve the system by triangularizing the augmented matrix and using back substitution.

Find the inverse of the 2 * 2 matrix using matrix multiplication, equality of matrices, and a system of equations.

Compute the determinant of the matrix and state whether an inverse matrix exists. Do not use a calculator.

Solve the system using substitution. Write your answer as an ordered pair.

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. -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.

Compute the determinant of the matrix and state whether an inverse matrix exists. Do not use a calculator.

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

For the system below, form the matrix equation AX = B. Compute the determinant of the coefficient matrix and determine if you can proceed. If possible, solve the system using the matrix equation.