Exam 9: Systems of Equations and Inequalities

The sales of various types of lawn and garden tools vary according to the season. At a certain home improvement store, the monthly sales H of garden hoes (hoes sold per month) declines from July to October whereas the monthly sales of lawn rakes R (rakes sold per month) increase during this same interval. The sales of these two items during the calendar months July-October are modeled by the equations: where t is the month (t = 7 corresponds to July). In which month does the number of rakes sold equal the number of hoes sold?

Determine which one of the ordered pairs below is a solution of the system of linear inequalities.

Solve the system by the method of substitution.

Use a graphing utility to graph the inequalities. Shade the region representing the solution set of the system.

A residential building contractor borrowed $30,000 to complete a new home. Some of the money was borrowed at 5%, some at 6%, and some at 8%. How much was borrowed at each rate if the annual interest owed was $1780 and the amount borrowed at 6% is four times more than the amount borrowed at 8%?

Find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints. (You should graph the feasible solutions on the grid below before you attempt to find the minimum and maximum values.)

Use a graphing utility to graph the inequality. Shade the region representing the solution.

Write the partial fraction decomposition of the rational expression.

Find the equation of the circle that passes through the points .

Solve the system by the method of elimination.

Derive a set of inequalities to describe the region.

Solve the system by the method of elimination.

Solve the system of linear equations.

Find the equation of the parabola that passes through the points.

For the given supply and demand equations, find the consumer surplus.

Applying Kirchhoff's Laws to the electrical network in the figure, the currents I₁, I₂, and I₃ are the solution of the system Find the currents.

Solve the system by the method of elimination.

Determine which ordered pair is a solution of the system.

Solve the system of linear equations.

Solve the system by the method of elimination.