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Sunday, 24 March 2013

Intermediate Algebra chapter 4

Third-Order Systems of Linear Equations
Chapter 4
General Ideas
"Third-Order Systems of Linear Equations" is just a fancy way of saying
  • 3 equations in 3 unknowns, or
  • 3 equations in 3 variables.
An example of a system of 3 equations in 3 unknowns:
3x + 7y - z = 6(1)
2x - 3y + 2z = 7(2)
-2x - 2y + 3z = 8(3)
The 3 unknows are x, y, and z. A solution will be an ordered triple (x, y, z).
Observe that for the above example:
  1. (1, 1, 4) satifies all 3 equations.
    • Plug x = 1, y = 1, and z = 4 into equations (1), (2), and (3), and all equations hold true.
  2. (0, 0, 1) does not satisfy any of the 3 equations, so it can't be the solution.
    • Plug x = 0, y = 0, and z = 1 into equations (1), (2), and (3), and none of the equations are true.
  3. Conclusion:
    • (1, 1, 4) is a solution to the example system of equations.
    • (0, 0, 1) is not a solution to the example system of equations.

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