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Chapter 5: Problem 38
Solve each system by the method of your choice. $$\left\\{\begin{array}{l} x^{2}-y^{2}-4 x+6 y-4=0 \\ x^{2}+y^{2}-4 x-6 y+12=0 \end{array}\right.$$
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Exercises 37-39 will help you prepare for the material covered in the first section of the next chapter. Solve the system: $$\left\\{\begin{aligned}w-x+2 y-2 z &=-1 \\\x-1 y+z &=1 \\\y-z &=1 \\\z-&-3\end{aligned}\right.$$ Express the solution set in the form \(\\{(\boldsymbol{x}, \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z})\\} .\) What makes it fairly easy to find the solution?
You are about to take a test that contains computation problems worth 6 points each and word problems worth 10 points each. You can do a computation problem in 2 minutes and a word problem in 4 minutes. You have 40 minutes to take the test and may answer no more than 12 problems. Assuming you answer all the problems attempted correctly, how many of each type of problem must you answer to maximize your score? What is the maximum score?
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 in Exercises 97-102. $$2 x+y \leq 6$$
Involve supply and demand. Although Social Security is a problem, some projections indicate that there's a much bigger time bomb ticking in the federal budget, and that's Medicare. In \(2000,\) the cost of Social Security was \(5.48 \%\) of the gross domestic product, increasing by \(0.04 \%\) of the GDP per year. In \(2000,\) the cost of Medicare was \(1.84 \%\) of the gross domestic product, increasing by \(0.17 \%\) of the GDP per year. a. Write a function that models the cost of Social Security as a percentage of the GDP \(x\) years after 2000 . b. Write a function that models the cost of Medicare as a percentage of the GDP \(x\) years after 2000 . c. In which year will the cost of Medicare and Social Security be the same? For that year, what will be the cost of each program as a percentage of the GDP? Which program will have the greater cost after that year?
Explain how to solve a system of equations using the addition method. Use \(3 x+5 y=-2\) and \(2 x+3 y=0\) to illustrate your explanation.
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