Math problems of the week: Systems of Equations in CPM vs. 1900's math

(Cross-posted at Out In Left Field)

1. The only systems of equations that students are required to solve algebraically in the CPM (College Preparatory Mathematics) Algebra Connections "Systems of Equations" chapter (published in 2006):

y = 1160 + 22x
y = 1900 - 15x

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y = 6 + 1.5x
y = 2x

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y = 2x -3
y = -x + 3

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y = 2x -3
y = 4x + 1

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y = 2x - 5
y = -4x - 2

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y = -x + 8
y = x -2

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y = -3x
y = -4x + 2

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y = 2x - 3
y = 2x + 1

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y = -4x -3
y = -4x + 1

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2. A subset of the over one hundred systems of equations in the Wentworth's New School Algebra "Simple Systems of Equations" chapter (published in 1898):

5x + 2y = 39
2x - y = 3

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x/3 + y/2 = 4/3
x/2 + y/3 = 7/6

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x + y - 8 = 0
y + z - 28 = 0
y + z - 14 = 0

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6x - 2y + 5z = 53
5x + 3y + 7 = 33
x + y + z = 5

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2x + 3y + 1 = 31
x - y + 3z = 13
10y + 5x - 2z = 48

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1/x + 2/y - 3/z = 1
5/x + 4/y + 6/z = 24
7/x - 8/y + 9/z = 14

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2/x - 3/y + 4/z = 2.9
5/x - 6/y - 7/x = -10.4
9/y + 10/z - 8/x = 14.9

3. Extra Credit:

(a) Discuss why CPM, but not New School Algebra, has to stipulate that the simultaneous equations be solved algebraically (rather than graphically or by "guess and check").

(b) Discuss the arithmetic and algebraic skills required by each problem set.

(c) Relate your answer in (b) to the final assignment in CPM's "Simultaneous Equations" chapter, the TEAM BRAINSTORM:

With your team, brainstorm a list for the following topics. Be as detailed as you can. How long can you make your list? Challenge yourselves. Be prepared to share you team's ideas with the class.

Topics: What have you studied in this chapter? What ideas and words were important in what you learned? Remember to be as detailed as you can.