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Math Help - elimination method; please help me solve

  1. #1
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    Lightbulb elimination method; please help me solve

    I keep getting different answers when I try to solve this problem, please help me!

    Eq 1: 4/3x+6y=(-1)
    Eq 2: 4x - 4y =(13/3)

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  2. #2
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    Hello, runner940!

    \begin{array}{cccc}\frac{4}{3}x+6y &=& \text{-}1 & {\color{blue}[1]}\\<br />
4x - 4y &=& \frac{13}{3} & {\color{blue}[2]} \end{array}
    First eliminate the fractions . . .

    \begin{array}{ccccc}\text{Multiply {\color{blue}[1]} by 3:} & 4x + 18y &=&\text{-}3 & {\color{blue}[3]} \\ \text{Multiply {\color{blue}[2]} by 3:} & 12x - 12y &=& 13 & {\color{blue}[4]} \end{array}

    \begin{array}{cccc}\text{Multiply {\color{blue}[3]} by 2:} & 8x + 36y &=& \text{-}6 \\ \text{Multiply {\color{blue}[4]} by 3:} & 36x - 36y &=& 39 \end{array}

    Add: . 44x \:=\:33 \quad\Rightarrow\quad\boxed{ x \:=\:\frac{3}{4}}

    Substitute into [1]: . 4(\tfrac{3}{4}) + 18y \:=\:\text{-}3 \quad\Rightarrow\quad18y \:=\:\text{-}6 \quad\Rightarrow\quad\boxed{ y \:=\:-\frac{1}{3}}

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