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Thread: fractions solve by substitution

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    fractions solve by substitution

    x/2-y/3=5/6
    x/5-y/4=29/10
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  2. #2
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    Quote Originally Posted by mafai44 View Post
    x/2-y/3=5/6
    x/5-y/4=29/10
    Hi mafai44,

    $\displaystyle [1]\:\: \frac{x}{2}-\frac{y}{3}=\frac{5}{6}$

    $\displaystyle [2]\:\: \frac{x}{5}-\frac{y}{4}=\frac{29}{10}$

    Multiply [1] by 6 and multiply [2] by 20

    $\displaystyle [3]\:\: 3x-2y=5$

    $\displaystyle [4]\:\: 4x-5y=58$

    Multiply [3] by 5 and multiply [4] by -2

    $\displaystyle [5]\:\: 15x-10y=25$

    $\displaystyle [6]\:\: -8x+10y=-116$

    Add [5] + [6]

    $\displaystyle 7x=-91$

    $\displaystyle \boxed{x=-13}$

    Using [3]

    $\displaystyle [3]\:\: 3(-13)-2y=5$

    $\displaystyle -39-2y=5$

    $\displaystyle -2y=44$

    $\displaystyle \boxed{y=-22}$



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