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Math Help - solve system

  1. #1
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    solve system

    I need help understanding how to find solutions to equational systems such as 4x-y+3z=-2
    3x+5y-z=15
    -2x+y+4z=14
    I have no idea how to find the solution, I have read over the examples in the book a thousand times and still have no clue as to how they come up with the solution, the formula they give is R1 + (-2)R2=R2
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  2. #2
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    Quote Originally Posted by mcooper2006 View Post
    I need help understanding how to find solutions to equational systems such as 4x-y+3z=-2
    3x+5y-z=15
    -2x+y+4z=14
    I have no idea how to find the solution, I have read over the examples in the book a thousand times and still have no clue as to how they come up with the solution, the formula they give is R1 + (-2)R2=R2
    The method of solution of a system like this involves eliminating x from
    equations 2 and 3 using equation 1.

    So we proceed by replacing equation 2 by 3 times equation 1 minus 4 times
    equation 2, which could be written as 3 R1 - 4 R2 = R2, that is the new
    second row equation R2 is:

    3(4x-y+3z)-4(3x+5y-z)=3(-2)-4(15)

    or (check the arithmetic here please):

    -23y + 13z = -66

    Now we proceed in a similar manner with the first and third equations. We
    add equation 1 to twice equation 3 to get a new equation 3, which we might
    write as R1 + 2 R3 = R3:

    (4x-y+3z) + 2(-2x+y+4z)=(-2) + 2(14),

    or:

    y + 11z = 26.

    So the system of equations now is:

    4x-y+3z=-2
    -23y + 13z = -66
    y + 11z = 26.

    Now the last two equations are a pair of simultaneous equations in two
    variables which you should be able to solve. Alternativly proceed as before
    using the new equation 2 to eliminate y from equation 3.

    Add equation 2 to 23 times equation 3 to get the new equation 3
    (or R2+23 R3=R3):

    (-23y + 13z) +23 (y + 11z) = -66 + 23 26,

    or:

    266 z = 532,

    or z=2.

    Now use this value of z in equation 2 to find y, and the values of z and y
    in equation 1 to find x.

    The full solution is shown in the attachment.

    RonL
    Attached Thumbnails Attached Thumbnails solve system-gash.jpg  
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