Exam 8: Systems of Equations and Inequalities

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? -

Find the value of the determinant. -

Write the word or phrase that best completes each statement or answers the question. -To raise money, a group of three friends is each trying to sell 100 candles. Each friend has a packagecontaining the same number of tapers, votives, and tealights. The tapers sell for $6.00 each, the votives sellfor $1.50 each, and the tealights sell for $0.75 each. Maya sold all of the candles to raise $431.25, Lorrin soldall of the tapers and tealights to raise $378.75, while Sara sold all the votives, all the tealights, and half ofthe tapers to raise $251.25. How many of each type of candle did each package contain?

Write the word or phrase that best completes each statement or answers the question. -An application of Kirchoffʹs Rules to the circuit shown results in the following system of equations: Find the currents

Solve the system of equations. -

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 7 inches longer than thewidth. Find the width.

Solve the system using the inverse matrix method. -

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Solve using elimination. -

Solve the problem. -The Family Fine Arts Center charges $22 per adult and $14 per senior citizen for its performances. On arecent weekend evening when 571 people paid admission, the total receipts were $9,378. How many whopaid were senior citizens?

Solve the linear programming problem. -A candy company has 135 pounds of cashews and 180 pounds of peanuts which they combine into twodifferent mixes. The deluxe mix has half cashews and half peanuts and sells for $6 per pound. Theeconomy mix has one third cashews and two thirds peanuts and sells for $5.90 per pound. How manypounds of each mix should be prepared for maximum revenue?

Solve the system of equations using substitution. -

Solve the linear programming problem. -Two kinds of crated cargo, A and B, are to be shipped by truck. The weight and volume of each type are givthe following table: The shipping company charges $75 per crate for cargo A and $100 per crate for cargo B. The truck has amaximum load limit of 7,200 pounds and 1,000 cubic feet. How many of each type of cargo should be shippto maximize profit for the shipping company?

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. C -

Graph the system of inequalities. -

Use the given matrices to compute the given expression. -Let A Find 4A + B.

Solve the system of equations by elimination. -

Solve the system of equations by substitution. -

Solve the system of equations by substitution. -

Write the partial fraction decomposition of the rational expression. -