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Find the complete solution of the linear system or show that its inconsistent?

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2x+3y-z=1

x+2y=3

x+3y+z=4

1 Answer

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  • 8 years ago
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    Standard form: 2x+3y-z=1; x+2y=3; x+3y+z=4;

    2, 3, -1, 1

    1, 2, 0, 3

    1, 3, 1, 4

    -----------------------

    substitute/eliminate x = -3/2y +1/2z+1/2

    2, 3, -1, 1

    0, 1/2, 1/2, 5/2

    0, 3/2, 3/2, 7/2

    -----------------------

    substitute/eliminate y = -z+5

    2, 0, -4, -14

    0, 1/2, 1/2, 5/2

    0, 0, 0, -4

    -----------------------

    2, 0, -4, -14

    0, 1/2, 1/2, 5/2

    0, 0, 0, -4

    -----------------------

    inconsistent system - no solutions.

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