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Chapter 7: Problem 95
Explain how to solve a system of equations using the substitution method. Use \(y=3-3 x\) and \(3 x+4 y=6\) to illustrate your explanation.
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Solve each system by the method of your choice. $$\left\\{\begin{array}{l} x^{2}+4 y^{2}=20 \\ x+2 y=6 \end{array}\right.$$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I use the same steps to solve nonlinear systems as I did to solve linear systems, although I don't obtain linear equations when a variable is eliminated.
Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user's manual for your graphing utility that describes how to shade a region. Then use your graphing utility to graph the inequalities. $$y \geq x^{2}-4$$
I graphed the solution set of \(y \geq x+2\) and \(x \geq 1\) without using test points.
a. Graph the solution set of the system: $$\left\\{\begin{array}{l}x+y \geq 6 \\\x \leq 8 \\\y \geq 5\end{array}\right.$$ b. List the points that form the corners of the graphed region in part (a). c. Evaluate \(3 x+2 y\) at each of the points obtained in \(\operatorname{part}(\mathrm{b})\)
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