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Math Help - simultaneous equations

  1. #1
    Newbie emma's Avatar
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    simultaneous equations

    Consider the simultaneous equations
    mx + 2y = 8
    4x - (2-m)y = 2m
    a) Find the values of m for which there are:
    i) no solutions
    ii) infinitely many solutions


    please explain how to do this, i am very confused, thank you.

    answer:
    i) m = -2
    ii) m = 4
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Quote Originally Posted by emma View Post
    mx + 2y = 8
    4x - (2-m)y = 2m

    You can turn these equations into the form y=mx+c giving
    mx + 2y = 8 \implies y=\frac{-m}{2}x+4

    and

     <br />
4x - (2-m)y = 2m \implies y = \frac{-4}{2-m}x+\frac{2m}{2-m}<br />

    Now equating coeffecients of x you solve for

     \frac{-m}{2} =  \frac{-4}{2-m}

    Cross multiplying

     -8 = -2m+m^2

    solving the quadratic gives

     m = -2 , 4

    So which one gives no solutions and which infinitely many solutions?

    The hint here is where the constant term in each equation is equal, this will yield infinitely many solutions
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