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Math Help - system!

  1. #1
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    Arrow system!

    Hello to everyone,

    I have some systems to solve in algebra. Please help me.

    1) λχ+2y=λ
    8y+λy=2λ

    and

    2) 7 + 4 = 47
    --- --- ---
    x-y x+y 15

    3 - 2 = 3
    --- --- ---
    x-y x+y 5


    they are fractions.
    I know the --- are fractions.



    Thanks.
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  2. #2
    Moo
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    Hello,

    1) λχ+2y=λ
    8y+λy=2λ
    What are the variables ?

    2) 7 + 4 = 47
    --- --- ---
    x-y x+y 15
    For this one...

    I notice that 15=5*3
    So if x-y=3 and x+y=5, you will see that it works... Perhaps there is another solution.

    Else put the fractions on the same denominator and solve..
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  3. #3
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    Hello, gdespina!

    2)\;\;\begin{array}{ccc}\dfrac{7}{x-y} + \dfrac{4}{x+y} &=&\cfrac{47}{15} \\ \\ \dfrac{3}{x-y} - \dfrac{2}{x+y} &=& \dfrac{3}{5} \end{array}

    Let: . \begin{array}{ccc}u &=&x-y \\ v &=& x+y \end{array}\;\;{\color{red}(A)}

    And we have: . \begin{array}{cccc}\dfrac{7}{u} + \dfrac{4}{v} &=& \dfrac{47}{15} & {\color{blue}[1]} \\ \\ \dfrac{3}{u} - \dfrac{2}{v} &=& \dfrac{3}{5} & {\color{blue}[2]} \end{array}


    \begin{array}{cccc}\text{Multiply {\color{blue}[2]} by 2:} & \dfrac{6}{u} - \dfrac{4}{v} &=&\dfrac{6}{5} \\ \\ \text{Add {\color{blue}[1]}:} & \dfrac{7}{u} + \dfrac{4}{v} &=&\dfrac{47}{15} \end{array}

    And we have: . \frac{13}{u} \:=\:\frac{13}{3}\quad\Rightarrow\quad\boxed{u \:=\:3}

    Substitute into [1]: . \frac{7}{3} + \frac{4}{v} \:=\:\frac{47}{15} \quad\Rightarrow\quad \frac{4}{v}\:=\:\frac{4}{5}\quad\Rightarrow\quad\b  oxed{v \:=\:5}


    Substitute into (A): . \begin{array}{ccc}x - y &=& 3 \\ x + y &=& 5 \end{array}
    . . . . . . . . . . Add: . . . . 2x \:=\:8 \qquad\Rightarrow\qquad \boxed{\begin{array}{ccc} x &=&4 \\ y&=&1 \end{array}}

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