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2 June, 17:56

What is the solution to the system?

5x-y+z=4

x+2y-z=5

2x+3y-3z=5

+2
Answers (1)
  1. 2 June, 21:21
    0
    Eliminate one variable at a time. We have three equations so we can solve for three variables.

    (5x-y+z=4) - 5 (x+2y-z=5) = - 11y+6z=-21

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

    Now using the two yz equations above to cancel out z

    (-11y+6z=-21) + 6 (-y-z=-5) = - 17y=-51

    -17y=-51 divide both sides by - 17

    y=3, making - y-z=-5 become:

    -3-z=-5, z=2, making 5x-y+z=4 become:

    5x-3+2=4

    5x-1=4

    5x=5

    x=1

    So the solution to the system of equations, (x, y, z) is (1,3,2)
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