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Thread: Infinite Number of Solutions

  1. #1
    Senior Member Stroodle's Avatar
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    Infinite Number of Solutions

    Find the value of $\displaystyle m$ for which the following simultaneous equations have an infinite number of solutions:

    $\displaystyle 3x+my=5$ and $\displaystyle (m+2)x+5y=m$

    So I know that they both need to be the same equation, but I can't work out a process for solving these.

    Thanks for your help
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  2. #2
    Member great_math's Avatar
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    $\displaystyle a_1x+b_1y=c_1$ and $\displaystyle a_2x+b_2y=c_2$ have infinite solutions if $\displaystyle \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

    From these equations..

    $\displaystyle a_1=3,b_1=m $ and $\displaystyle c_1=5$

    $\displaystyle a_2=m+2,b_2=5,c_2=m$

    so $\displaystyle \frac3{m+2}=\frac m{5}$

    $\displaystyle \Rightarrow 15=m^2+2m$

    $\displaystyle \Rightarrow m^2+2m-15=0$

    $\displaystyle \Rightarrow m=\{-5,3\}$--------------[1]

    Also, $\displaystyle \frac m{5}=\frac5{m}$

    $\displaystyle \Rightarrow m=\pm 5$-----------------[2]

    From equation [1] and equation [2] we get $\displaystyle m=-5$
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  3. #3
    Senior Member Stroodle's Avatar
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    Awesome.
    Too easy

    Thanks for that!
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