Question

Just a general question

Answer 1

Is it always true , that to solve a system of equations , the equations should be equal to number of unknowns

Answer 2

Not necessarily. You can have other restrictions. What if you are only looking for Diophantine solutions or prime numbers that satisfy a system of equations. I guess if you're asking in general then perhaps I'm missing the point.

If it's just a system of linear equations, you can solve if the number of equations is equal to the number of unknowns.

Answer 3

Because , i solved a question of three unknowns , with two equations

Answer 4

And the answer was correct.

Answer 5

y=2x+3
y=2x-9

This is an unsolvable equation. In fact there are over defined equations where there are multiple answers, such as when you are trying to find the least squares curve to fit data.

In fact, you showed me a single equation before that had 3 unknowns and was solvable, since the only answer was prime numbers. So often times you can have restrictions that aren't equations which give you a unique solution just because of the boundaries. I think it was:

p^2-q^2=r

what are all the solutions where p, q, and r are all prime?

Answer 6

i got the point.
Just asking what is a diaphontine equn
forgive for spelling

Answer 7

Just an equation where the answers are only integers. For instance:

\[\LARGE y^x=x^y-1\] has only one diophantine solution: \[\LARGE 2^3=3^2-1\] Or maybe you're interested in \[\LARGE a*b*c=a+b+c\] you can have any order of \[\LARGE 1*2*3=1+2+3\] along with the trivial solution of all 0's.

Answer 8

so only integer sollutions , this is interesting hmm

Answer 9

ganeshie8 told me something about Pell's equation long back this looks similar

Answer 10

Yeah, also 3^2+4^2=5^2 is one of many possible Diophantine solutions to the Pythagorean Theorem, these are called Pythagorean Triples. Obviously Diophantine equations are common because there are a lot of things that don't make sense to have a fraction or non-integer amount of.

Answer 11

Like in chemistry, when you balance a chemical equation you either have a molecule or you don't, there's really no inbetween even though sometimes they might write it with fractions for some kind of mathematical simplicity of calculating enthalpy changes or something like that.

Answer 12

hmm , it might have a lot of practical uses

Answer 13

I have more than 2.5 brothers and less than 3.999 brothers. How many brothers can I possibly have?

Answer 14

1

Answer 15

hhaaha

Answer 16

lol 2.5<1? XD

Answer 17

i meant 3 lol

Answer 18

i don't know what i was thinking of

Answer 19

i was thinking of 1 integer value lies between thos numbers , so i wrote one brother

Answer 20

Hahaha but yeah you get the point, definitely useful! You've been thinking in terms of Diophantine equations your whole life. I've never once thought, "hmm, if I have a bag full of red and blue marbles, what's the probability of pulling out a half of a red marble?" lol

Answer 21

that is useless

Answer 22

hehe

Answer 23

Actually, some things you even sort of don't think of in terms of non-diophantine things because it's impossible as far as I can see.

If x*x*x=x^3 means you are multiplying a number by itself 3 times. Then what is x^1/2 ? Obviously x^1/2 is the square root, but it's not quite clear how you could multiply a number by itself just half of a time!

Answer 24

maybe our vision is restricted

Answer 25

I think it is. I see no reason why we shouldn't just always extend ourselves further. Why don't we ever take the 1/2 derivative? Or 1/2 factorial? Well, in fact we can do this. But I won't get into that now haha.

Answer 26

Unless you want me to. Otherwise if you ever get bored, look up the gamma function or fractional calculus, pretty interesting.

Answer 27

not for now , but after i mover to higher classes