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Problem 10

Find all solutions of the given system of equations and check your answer graphically. $\begin{aligned}-\frac{2 x}{3}+\frac{y}{2} &=-\frac{1}{6} \\ \frac{x}{4}-y &=-\frac{3}{4} \end{aligned}$

Expert verified

The solution of the given system of equations is \((5, \frac{5}{3})\). To check this answer graphically, graph the lines with equations \(y = \frac{1}{3}x + \frac{1}{3}\) and \(y = \frac{1}{4}x + \frac{3}{4}\) and ensure that they intersect at the point \((5, \frac{5}{3})\).

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Chapter 2

Intramural Sports The best sports dorm on campus, Lombardi House, has won a total of 12 games this semester. Some of these games were soccer games, and the others were football games. According to the rules of the university, each win in a soccer game earns the winning house 2 points, whereas each win in a football game earns them 4 points. If the total number of points Lombardi House earned was 38 , how many of each type of game did they win?

Chapter 2

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Chapter 2

Give an example of a system of three linear equations with he general solution \(x=1, y=1+z, z\) arbitrary. (Check your system by solving it.)

Chapter 2

Select one: Multiplying both sides of a linear equation by a nonzero constant results in a linear equation whose graph is (A) parallel to (B) the same as (C) not always parallel to (D) not the same as the graph of the original equation.

Chapter 2

In 2007, total revenues from sales of recorded rock, religious, and classical music amounted to \(\$ 4\) billion. Religious music brought in twice as much as classical music, and rock music brought in \(\$ 3\) billion more than religious music. \({ }^{12}\) How much revenue was earned in each of the three categories of recorded music?

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