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In Lewis Carroll's Through the Looking Glass, the Following dialogue takes place: Tweedledum (to Tweedledee): The sum of your weight and twice mine is 361 pounds. Tweedledee (to Tweedledum): Contrawise, the sum of your weight and twice mine is 362 pounds. Find the weight of each of the two characters. (IMAGE CAN NOT COPY)

Write a system of inequalities that describes all the points in quadrant III of a rectangular coordinate system.

The following system models the winning times, \(y,\) in seconds, in the Olympic 500 -meter speed skating event \(x\) years after 1970: $$\left\\{\begin{array}{l}y=-0.19 x+43.7 \\ y=-0.16 x+39.9\end{array}\right.$$ Use the slope of each model to explain why the system has a solution. What does this solution represent?

Promoters of a rock concert must sell at least \(25,000\) tickets priced at \(\$ 35\) and \(\$ 50\) per ticket. Furthermore, the promoters must take in at least \(\$ 1,025,000\) in ticket sales. Write and graph a system of inequalities that describes all possibilities for selling the \(\$ 35\) tickets and the \(\$ 50\) tickets.

Determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. Each equation in a system of linear equations has infinite many ordered-pair solutions.