# confusing algebra

This topic is 3300 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

ok, I've started a problem with two equations with two unknows but somehow I have got trapped. I started with these two equations:
x1 + ua(x2 - x1) = x3 + ub(x4 - x3)

y1 + ua(y2 - y1) = y3 + ub(y4 - y3)

I then isolated the ub unknown:

y1 - y3 + ua(y2 - y1)
---------------------   = ub
y4 - y3

x1 - x3 + ua(x2 - x1)
---------------------   = ub
x4 - x3


then I found the common denominator for each equation:

(y1 - y3)(x4 - x3) + ua(y2 - y1)(x4 - x3)
-----------------------------------------
(y4 - y3)(x4 - x3)

(x1 - x3)(y4 - y3) + ua(x2 - x1)(y4 - y3)
-----------------------------------------
(x4 - x3)(y4 - y3)


then subtracted them to give:

(y1 - y3)(x4 - x3) - (x1 - x3)(y4 - y3) + ua(y2 - y1)(x4 - x3) - ua(x2 - x1)(y4 - y3)
----------------------------------------------------------------------------------  = 0
(y4 - y3)(x4 - x3)


then I separated the addition and got rid of the denominator to give me:

(y1 - y3)(x4 - x3) - (x1 - x3)(y4 - y3) =   - ua(y2 - y1)(x4 - x3) + ua(x2 - x1)(y4 - y3)


but I think I've done something wrong somewhere, the correct answer should be:

(x4 - x3)(y1 - y3) - (y4 - y3)(x1 - x3)
---------------------------------------
(y4 - y3)(x2 - x1) - (x4 - x3)(y2 - y1)


can anyone tell me where I went wrong?

##### Share on other sites
If you solve your equation by ua you will obtain:

(x4 - x3)(y1 - y3) - (y4 - y3)(x1 - x3)

--------------------------------------- = ua

(y4 - y3)(x2 - x1) - (x4 - x3)(y2 - y1)

##### Share on other sites
do you know where I went wrong in my attempt?

##### Share on other sites
Quote:
 Original post by staticVoid2....then I separated the addition and got rid of the denominator to give me:(y1 - y3)(x4 - x3) - (x1 - x3)(y4 - y3) = - ua(y2 - y1)(x4 - x3) + ua(x2 - x1)(y4 - y3)can anyone tell me where I went wrong?

If you take that equation and isolate ua you get:
(y1 - y3)(x4 - x3) - (x1 - x3)(y4 - y3) = ua(-(y2 - y1)(x4 - x3) + (x2 - x1)(y4 - y3)) <=>(y1 - y3)(x4 - x3) - (x1 - x3)(y4 - y3) = ua((x2 - x1)(y4 - y3) - (y2 - y1)(x4 - x3)) <=> (y1 - y3)(x4 - x3) - (x1 - x3)(y4 - y3)----------------------------------------- = ua (x2 - x1)(y4 - y3) - (y2 - y1)(x4 - x3)

Since the order of multiplication doesn't matter you can move around the terms a bit to get:
 (x4 - x3)(y1 - y3) - (y4 - y3)(x1 - x3)----------------------------------------- = ua (y4 - y3)(x2 - x1) - (x4 - x3)(y2 - y1)

So you've done nothing wrong, you just didn't go all the way.

##### Share on other sites
Closing thread. School problems are a violation of forum policy.

Forum FAQ