I have 2 2d line equations in general form (Ax+By+C=0) and I would like to find the point of intersection (if any). How can I do this? I started to write it out on paper and gave up because I would have had to simplify a huge equation. I know there is a simple solution, so if you are man(or women) enough to take the math challenge, please post what you think is the quickest solution.
Pseudo

# the math challenge

Started by Pseudo, Jul 21 2001 12:46 PM

4 replies to this topic

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#2
Members - Reputation: **122**

Posted 21 July 2001 - 12:57 PM

Lets say we have two lines:

y = mx + b

y = 3x + 3

y = 4x + 1

To find the point of intersection we arrange them like this:

x + y = b

-3x + y = 3

-4x + y = 1

This is a systems of equation. What we have to do is have either the x or the y on the top and bottom being the inverse value. So lets use the x:

12x - 4y = -12

-12x + 3y = 3

All I did was multiply the top by - 3, and the bottom by + 3. This gives us an equation we can solve. We now cross of the zeroing xs, add the ys and add the ending term:

0x - 1y = -9

-1y = -9

y = 9

Now to find the x point, we take a line and substitute in for y and solve for x.

9 = 3x + 3

6 = 3x

2 = x

(2, 9) is the point of intersection for the two lines defined by: y = 3x + 3, y = 4x + 1. Hope this helped. I did this based on memory so I''m not sure if it is all entirely correct.

y = mx + b

y = 3x + 3

y = 4x + 1

To find the point of intersection we arrange them like this:

x + y = b

-3x + y = 3

-4x + y = 1

This is a systems of equation. What we have to do is have either the x or the y on the top and bottom being the inverse value. So lets use the x:

12x - 4y = -12

-12x + 3y = 3

All I did was multiply the top by - 3, and the bottom by + 3. This gives us an equation we can solve. We now cross of the zeroing xs, add the ys and add the ending term:

0x - 1y = -9

-1y = -9

y = 9

Now to find the x point, we take a line and substitute in for y and solve for x.

9 = 3x + 3

6 = 3x

2 = x

(2, 9) is the point of intersection for the two lines defined by: y = 3x + 3, y = 4x + 1. Hope this helped. I did this based on memory so I''m not sure if it is all entirely correct.

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#3
Anonymous Poster_Anonymous Poster_*
Guests - Reputation:

Posted 21 July 2001 - 01:00 PM

I''d rewrite each formula so that a single variable (x or y) was on one side. I will pick y:

Ax + By + C = 0

By = -Ax - C

y = -Ax/B - C/B (y=mx+b format)

Do that for each line, then set the y of one line = to the y of the other line, so you will get something like:

4x + 5 = 5x + 3

Then solve for x:

5 - 3 = 5x - 4x

2 = x