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Say i have 2 equations, s =t and 1-s = t-1.

Normally one would solve the equations simply but subbing in S=t into the other equation and obtain t = s = 1.

However, if i were to slightly rearrange this equation:

1-s = t-1

I can obtain this :

-1(s-1) = (t-1)

-1 = (t-1)/(s-1), wouldn't this not make sense if i sub s=t into it?

And i am anticipating that some would point out that by rearranging the equation i divided by 0. So the whole thing is not valid.

However what if i rewrote my whole post and state first that initially i have 2 equations, s=t and 1 = (t-1)/(1-s) and i wish to solve this.

Then i would have solve it like this :

1 = (t-1)/(1-t)

1-t = t-1

t=1 = s

However if this is the case then wouldn't the original equation 1 = (t-1)/(1-s) is self is invalid?

What is wrong here? or did i go something wrongly?

By the way, i came across this thing as i am doing my vectors -Planes tutorial.

Any help will be greatly appreciated.