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Math Help - Infinite Number of Solutions

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

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

    3x+my=5 and (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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    a_1x+b_1y=c_1 and a_2x+b_2y=c_2 have infinite solutions if \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}

    From these equations..

    a_1=3,b_1=m and c_1=5

    a_2=m+2,b_2=5,c_2=m

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

    \Rightarrow 15=m^2+2m

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

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

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

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

    From equation [1] and equation [2] we get 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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