Algebra 2

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What would be the simplest way to eliminate one of the variables? Below is a system of three equations in three variables:
1. x+y+3z=7
2. 2x-4y+z=7
3. 3x+5y-4z=-6

  • Algebra 2 -

    one simple way is to substitute x #1 into #2 and #3:

    2(7-y-3z) - 4y + z = 7
    3(7-y-3z) + 5y - 4z = -6
    which gives you

    -6y -5z = -7
    2y - 13z = -27

    now we see 2y = 13z-27, so

    -3(13z-27) - 5z = -7
    -44z = -88
    z = 2

    so, y = (26-27)/2 = -1/2
    and x = 7-(-1/2)-6 = 1/2

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