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Maximizing Area and Solving Systems of Linear Equations

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1) You have 80 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

2) A rain gutter is made from sheets of aluminum that are 12 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow. What is the maximum cross-sectional area?

3) Determine whether the given ordered pair is a solution of the system.
(8,5)
5x - 4y =20
3 y = 2X + 1

4) Solve by the substitution method.
2X + 5y =1
-x + 6y =8

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Maximizing Area and Solving Systems of Linear Equations are investigated. The solution is detailed and well presented.

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