Chapter 2: Chapter 2

Find all solutions of the given system of equations and check your answer graphically. \(2 x-3 y=1\) \(6 x-9 y=3\)

Use Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand, and others using technology. HINT [See Examples 1-6.] $$ \begin{aligned} x+2 y &=1 \\ 3 x-2 y &=-2 \\ 5 x-y &=\frac{1}{5} \end{aligned} $$

Use Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand, and others using technology. HINT [See Examples 1-6.] $$ \begin{array}{r} 0.5 x+0.1 y=1.7 \\ 0.1 x-0.1 y=0.3 \\ x+y=\frac{11}{3} \end{array} $$

The Enormous State University Good Works Society recently raised funds for three worthwhile causes: the Math Professors' Benevolent Fund (MPBF), the Society of Computer Nerds (SCN), and the NY Jets. Because the society's members are closet jocks, the society donated twice as much to the NY Jets as to the MPBF, and equal amounts to the first two funds (it is unable to distinguish between mathematicians and nerds). Further, for every \(\$ 1\) it gave to the MPBF, it decided to keep \(\$ 1\) for itself; for every \(\$ 1\) it gave to the SCN, it kept \(\$ 2\), and for every \(\$ 1\) to the Jets, it also kept \(\$ 2\). The treasurer of the Society, Johnny Treasure, was required to itemize all donations for the Dean of Students, but discovered to his consternation that he had lost the receipts! The only information available to him was that the society's bank account had swelled by \(\$ 4,200\). How much did the society donate to each cause?

Find all solutions of the given system of equations and check your answer graphically. \(2 x+3 y=2\) \(-x-\frac{3 y}{2}=-\frac{1}{2}\)

Use Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand, and others using technology. HINT [See Examples 1-6.] $$ \begin{aligned} -0.3 x+0.5 y &=0.1 \\ x-\quad y &=4 \\ \frac{x}{17}+\frac{y}{17} &=1 \end{aligned} $$

Use Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand, and others using technology. HINT [See Examples 1-6.] $$ \begin{aligned} -x+2 y-z &=0 \\ -x-y+2 z &=0 \\ 2 x &-z=4 \end{aligned} $$

Use technology to obtain approximate solutions graphically. All solutions should be accurate to one decimal place. \(\begin{aligned} 2 x+8 y &=10 \\ x+y &=5 \end{aligned}\)

Suppose that, on a 2,000-mile Miami-Memphis flight, Continental, Delta, and Southwest flew a total of 200 empty seats, costing them a total of $\$ 51,500$. If Delta had twice as many empty seats as Southwest, how many empty seats did each of these three airlines carry on its flight?

Use technology to obtain approximate solutions graphically. All solutions should be accurate to one decimal place. \(2 x-y=3\) \(x+3 y=5\)