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Math Help - simultaneous equations in matrices - 3 solutions

  1. #1
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    simultaneous equations in matrices - 3 solutions

    For what value(s) of m will the system of equations,

    x+my=2
    (m-1)x+2y=m

    have:

    a) a unique solution?
    b) no solution?
    c) an infinite number of solutions?
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  2. #2
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    Quote Originally Posted by shawli View Post
    For what value(s) of m will the system of equations,

    x+my=2
    (m-1)x+2y=m

    have:

    a) a unique solution?
    b) no solution?
    c) an infinite number of solutions?
    Try solving it! For example, you can multiply the first equation by 2 and the second equation by m and subtract to eliminate y:
    (2x+ 2my)- (m(m-1)x+ 2my)= 4- m^2

    (2- m^2+ m)x= 4- m^2

    x= \frac{m^2- 4}{m^2- m- 2}
    Now, if the denominator is not 0, there is a unique solution. If the denominator is 0 and the numerator is not, there is no solution. If both numerator and denominator are 0, there are an infinite number of solutions.
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