Algebra Question

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I did a problem and used the substitution method and it took me forever to solve by hand. Is there a shorter way to show how this problem was done. The problem was
x+y+z=7,x-y+2z=7,2x+y+3z=15

The final answer came out to be
x=4
z=2
y=1

  • Algebra Question -

    This problem just "begs" to be done by elimination, look at the y values

    add #1 and #2 2x + 3z = 14 #4
    add #2 and #3 3x + 5z = 22 #5

    triple #4 -- 6x + 9z = 42
    double #5 -- 6x + 10z = 44

    subtract #5 - #4
    z = 2

    sub into #4 -- 2x+6 = 14 , x = 4
    back into #1
    4 + y + 2 = 7
    y = 1

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