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Math Help - Determine m

  1. #1
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    Determine m

    THere are given lines p1: \left( {m - 6} \right)x + \left( {m - 1} \right)y + 13 = 0 and p2:  \left( {2m + 1} \right)x + 3my - 9 = 0
    Determine m so that lines p1 and p2 have one common point F and F is a point of this line q: 2x+y-5
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  2. #2
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    Quote Originally Posted by beq!x View Post
    THere are given lines p1: \left( {m - 6} \right)x + \left( {m - 1} \right)y + 13 = 0 and p2:  \left( {2m + 1} \right)x + 3my - 9 = 0
    Determine m so that lines p1 and p2 have one common point F and F is a point of this line q: 2x+y-5
    2x+ y- 5 isn't a line. Do you mean 2x+ y- 5= 0?

    For the first line, y= -[(m-6)/(m-1)]x- 13/(m-1) (as long as m-1 is not 0). For the second line, y= -[(2m+1)/2m]x+ 3/m. At any point where they intersect y= -[(m-6)/(m-1)]x- 13/(m-1)= -[(2m+1)/2m]x+ 3/m. Solve that for x, in terms of m, of course, and use either of the two equaitions to determine y. Finally, put those values of x and y into 2x+ y- 5= 0 to get a single equation for m.
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  3. #3
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    yes i mean 2x+ y- 5= 0
    but why we have to do this: y= -[(m-6)/(m-1)]x- 13/(m-1)= -[(2m+1)/2m]x+ 3/m ?
    and i tried in this way but i didn't come to these solutions m=2 and m=2.8 that are in the book.
    im confused with this :S
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  4. #4
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    1. Solve p1 for y
    2. Solve p2 for y
    3. If the lines intersect then the y-values must be equal.
    4. You'll get HallsofIvy's equation with a slight change:
    -[(m-6)/(m-1)]x- 13/(m-1)= -[(2m+1)/(3m)]x+ 3/m

    5. Proceed as HallofIvy has suggested.
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  5. #5
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    thank you guys
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