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Algebra II

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Right now we're doing systems of Linear Equations in Three Variables. It says to solve the following system:
x - y + 3z = 4
x + 2y - z = -3
4x + 3y + 2z = -5

Whatever I try with this problem (and the others like it) it comes out wrong. I've had about one success.
And Is there a certain order you're supposed to solve them in? Or does that not make a difference?

  • Algebra II -

    I will assume you are using elimination, although there are several other methods.

    In elimination, you first have to decide which variable you want to eliminate. Usually that is determined by choosing the simplest coefficients, in this case I would go for z
    1st: x-y + 3z = 4
    2nd times 3: 3x + 6y - 3z = -9
    add them 4x + 5y = -5 (#4)

    2nd times 2: 2x + 4y - 2z = -6
    3rd: 4x + 3y + 2z = -5
    add them 6x + 7y = -11 (#5)
    #4 times 3 : 12x + 15y = -15
    #5 times 2: 12x + 14y = -22
    subtract them
    y = 7
    back into #4 : 4x + 35 = -5
    4x = -40
    x = -10
    back into #1 : -10 - 7 + 3z = 4
    3z = 21
    z = 7

    x = -10 , y = 7, z = 7

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