Pre-Calculus

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Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2

I really need help..
1 1 1 -5
1 -1 3 -1
4 1 1 1 -2


I've done so many different methods to solve this and I get stuck..

  • Pre-Calculus -

    agree with

    1 1 1 -5
    1 -1 3 -1
    4 1 1 -2 -----> you had an extra 1 in there

    1 1 1 -5
    0 2 -2 -4 #1 - #2
    0 3 3 -18

    1 1 1 -5
    0 1 -1 -2 #2 divided by 2
    0 1 1 -6 #3 divided by 3

    1 1 1 -5
    0 1 -1 -2
    0 0 -2 4 #2 - #3

    1 1 1 -5
    0 1 -1 -2
    0 0 1 -2

    from #3:
    z = -2
    in #2:
    y - z = -2
    y + 2 = -2
    y = -4

    in #1
    x + y + z = -5
    x - 4 - 2 = -5
    x = 1

    x = 1, y = -4, z = -2

  • Pre-Calculus -

    thank you!

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