Math (linear algebra)

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Solve the system of equation.

x- 2y+ 3z = 5
3x + y = -5
-2x+y + z = 8

  • Math (linear algebra) -

    x- 2y+ 3z = 5
    3x + y = -5
    -2x+y + z = 8

    First thing to check is that we have three equations and three unknowns, which is fine. If there are more unknowns than equations then there is a problem with the question.

    x- 2y+ 3z = 5
    3x + y = -5
    -2x+y + z = 8

    we need to eliminate one unknown by combining pairs of equations. Lets say we remove the y terms.

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

    x- 2y+ 3z = 5
    6x + 2y = -10

    Add these two and y terms are removed.

    7x+3z=-5


    Do the same with, but this time subtract the two and the y terms are removed

    3x + y = -5
    -2x+y + z = 8

    5x-z=-13

    We now have two equations and two unknwons

    7x+3z=-5
    5x-z=-13 (multiply by 3)

    7x+3z=-5
    15x-3z=-39

    and add

    22x=-44, so x=-2

    substitute in here to find y
    3x + y = -5

    the substitute in one of the above to find z

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