Posted by Parker on Wednesday, July 12, 2006 at 3:10pm.
If you have these three origins:
How do you find the last point where the two lines intersect?
Would really appreciate the help.
Parker, I'm not quite sure what the question asks. Three origins? Is this standard analytic geometry we're doing?
I see what appear as 3 ordered pairs. I'm not sure what 2 lines you have in mind. Are the coordinate axis involved somehow?
Maybe I missed a lesson somewhere, so enlighten me a little, please.
I got it from the intersection of the 2 lines (one for Metal and one for Labor). One line hit the axes at 1,187 and at 863. The other hits the axes at 952 and 1,111. Now I have to figure out where the two lines intersect.
If I could get the equations of those 2 lines and set them equal to each other -- and that's the point where they intersect.
From here, I could have one line:
Y = (- 1,187/863) (X) + 1,187
and the other line is is:
Y = (-952/1,111) (X) + 952
And, then get an X (number of deluxe) and a Y (number of standard). But don't know how to solve.
Ok Parker, I have a better grasp of things now.
Essentially you have 2 eq's in 2 var's (equations, variables)
Now you want to rearrange things a little.
(1,187/863)X + y = 1,187
(952/1,111)X + Y = 952
Does this look familiar?
With this type of system there can be 0,1, or infinitely many solutions as follows:
0 - the lines are parallel
1 - distinct non-parallel lines
infinite - the lines coincide (same line - different "names")
By 'eyeball analysis' it appears to me there should be 1 solution. Prove it. Write back if you need further help or want to verify work. Remember: after you solve for x say, solve for the y value too -very important.)
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