college algebra

Solve the system of linear equations and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express x, y, and z in terms of the parameter a.)

x +2z=5
3x-y-z=12
6x-y-5z=27

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asked by Keith
  1. in Matrix form:
    1,0,2 P5
    3,-1,-1:12
    6,-1,-5:27


    so subtracting equation 2 from 3
    we get equation 1, and
    3,0,-4:15
    Now multiply equation 1 by a factor of 2 to get
    2,0,4:10
    now adding those two equations
    5,0,0:25 orx=5
    putting that into equation 1, we get z=0
    putting those into equation 2 we get
    15-y-0=12 or y=3
    and that checks in equation 3.

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  2. subtract the 2nd equation from the 3rd equation

    solve the two remaining x and z equations with substitution or elimination

    x + 2z = 5

    3x - 4z = 15

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    posted by Scott
  3. but what are the parameters of a?

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    posted by Keith
  4. only if the system is dependent ... which it isn't

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    posted by Scott

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