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Magazine Problem 42
What is one of the drawbacks to solving a system of linear equations by graphing?
Problem 47
Two types of tickets are to be sold for a concert. One type costs \(\$ 15\) per ticket and the other type costs \(\$ 25\) per ticket. The promoter of the concert must sell at least 15,000 tickets, including at least 8000 of the \(\$ 15\) tickets and at least 4000 of the \(\$ 25\) tickets. Moreover, the gross receipts must total at least \(\$ 275,000\) in order for the concert to be held. Write a system of linear inequalities that describes the different numbers of tickets that can be sold.
Problem 51
Explain the meaning of the term half-plane. Give an example of an inequality whose graph is a half-plane.
Problem 52
Can the solution of a system of linear inequalities be a line? Explain.
Problem 53
Can the solution of a system of linear inequalities be a single point? Explain.
Problem 53
Describe any advantages of the method of substitution over the graphical method of solving a system of linear equations.
Problem 65
In Exercises \(63-66\), solve the equation. $$ z^{2}-4 z-12=0 $$
