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Math Help - row operation

  1. #1
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    row operation

    solve the system.
    x1 -3x2 = 5
    -x1 +x2 +5x3 = 2
    x2 + x3 = 0
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  2. #2
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    Hello, m777!

    This one isn't too hard.
    . . Exactly where is your difficulty?


    Solve the system

    . . \begin{array}{cccccccc}x &-& 3y & & & = &  5 & \quad{\color{blue}[1]} \\ -x &+ & y & + &5z & = & 2 & \quad{\color{blue}[2]}\\& & y & + & z & =&  0 & \quad{\color{blue}[3]}\end{array}

    Add [1] and [2]: . -2y + 5z \:=\:7

    Multiply [3] by 2: - - 2y + 2z \:=\:7

    Add: . 7z \:=\:7\quad\Rightarrow\quad\boxed{ z \:=\:1}

    Substitute into [3]: . y + 1:=\:0\quad\Rightarrow\quad\boxed{ y \:=\:-1}

    Substitute into [1]: . x -3(-1)\:=\:5\quad\Rightarrow\quad \boxed{x \:=\:2}

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