THere are given lines p1: and p2:

Determine so that lines p1 and p2 have one common pointFandFis a point of this line q:

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- March 30th 2009, 01:56 AMbeq!xDetermine m
THere are given lines p1: and p2:

Determine so that lines p1 and p2 have one common point**F**and**F**is a point of this line q: - March 30th 2009, 05:39 AMHallsofIvy
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. - March 30th 2009, 01:54 PMbeq!x
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 - March 30th 2009, 11:44 PMearboth
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)/(**3**m)]x+ 3/m

5. Proceed as HallofIvy has suggested. - April 1st 2009, 10:22 AMbeq!x
thank you guys :D