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Thread: [SOLVED] More Sim Equations

  1. #1
    ADY
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    Arrow [SOLVED] More Sim Equations

    Please help with:


    $\displaystyle X + 7Y = 6 $
    $\displaystyle 3X + 5Y = 14$

    I still cant get my head around this!

    Thanks in advance!

    ADY
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  2. #2
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    For example multiply the first equation (both sides) by 3: $\displaystyle 3X + 21Y = 18 $ and subtract from this the other equation: $\displaystyle (3-3)X+(21-5)Y=18-14 \Leftrightarrow 16Y=4\Leftrightarrow Y=\frac {4}{16}=\boxed{\frac 14=0.25}$ which you can substitute in one of the original equation: $\displaystyle X+7\cdot\frac 14=6\Leftrightarrow X=6-\frac 74=\boxed{\frac {17}4=4.25}$.
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  3. #3
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    Quote Originally Posted by ADY View Post
    Please help with:


    $\displaystyle X + 7Y = 6 $
    $\displaystyle 3X + 5Y = 14$

    I still cant get my head around this!

    Thanks in advance!

    ADY

    $\displaystyle 3x+21y=18 $ -------------1

    $\displaystyle 3x+5y=14$ --------------2

    2-1

    Therefore , 16y=4 , y=1/4 , then continue to solve for x .
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  4. #4
    ADY
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    $\displaystyle
    x = \frac{17}{4}, y = \frac{1}{4}
    $

    ?
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  5. #5
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    Quote Originally Posted by ADY View Post
    $\displaystyle
    x = \frac{17}{4}, y = \frac{1}{4}
    $

    ?
    Yeah.
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  6. #6
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    Quote Originally Posted by ADY View Post
    Please help with:


    $\displaystyle X + 7Y = 6 $
    $\displaystyle 3X + 5Y = 14$

    I still cant get my head around this!

    Thanks in advance!

    ADY
    try this, substitution method

    $\displaystyle X + 7Y = 6 $

    $\displaystyle 3X + 5Y = 14$

    $\displaystyle x=6-7y$

    $\displaystyle 3(6-7y)+5y=14$

    $\displaystyle 18-21y+5y=14$

    $\displaystyle 18-14=21y-5y$

    $\displaystyle 4=16y$

    $\displaystyle y=\frac{1}{4}$

    then substitute

    $\displaystyle x+7y=6$

    $\displaystyle x+\frac{7}{4}=6$

    $\displaystyle x=6-\frac{7}{4}$

    $\displaystyle x=\frac{24-7}{4}$

    $\displaystyle x=\frac{17}{4}$

    check

    $\displaystyle \frac{17}{4}+7{1}{4}=6$

    $\displaystyle \frac{24}{4}=6$

    $\displaystyle 6=6$

    $\displaystyle 3x+5y=14$

    $\displaystyle 3*\frac{17}{4}+5*\frac{1}{4}=14$

    $\displaystyle \frac{51+5}{4}=14$

    $\displaystyle \frac{56}{4}=14$

    $\displaystyle 56=56$

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