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Chapter 4: Problem 54
What is a system of linear equations? Provide an example with your description.
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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.
In Exercises \(45-56,\) solve each system by the method of your choice. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. Explain why you selected one method over the other two. $$\left\\{\begin{array}{l} y=2 x+1 \\ y=2 x-3 \end{array}\right.$$
Read Exercise \(72 .\) Then use a graphing utility to solve the systems. $$\left\\{\begin{array}{l}x+2 y=4 \\ x-y=4\end{array}\right.$$
In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} x-y=-3 \\ \frac{x}{9}-\frac{y}{7}=-1 \end{array}\right.$$
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?
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