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May 31st, 2017, 09:09 AM   #1
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Simultaneous equations.

Can there be more than two simultaneous
equations to be solved?

If yes, How many ? If Simultaneous equations > 2, How they can be simplified?

If No,Why Simultaneous equations cannot be greater than 2?

Thanks & Regards,
Prashant S Akerkar

Last edited by prashantakerkar; May 31st, 2017 at 09:11 AM.
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May 31st, 2017, 09:44 AM   #2
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Enough is enough.

Go away.

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May 31st, 2017, 09:53 AM   #3
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Quote:
Originally Posted by prashantakerkar View Post
Can there be more than two simultaneous
equations to be solved?
Why did you originally post this under calculus? Why are you posting so many questions that you could easily resolve by use of a search engine?
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May 31st, 2017, 09:58 AM   #4
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Quote:
Originally Posted by prashantakerkar View Post
Can there be more than two simultaneous
equations to be solved? YES

If yes, How many ? ANY FINITE NUMBER

If Simultaneous equations > 2, How they can be simplified? SUBSTITUTION

If No,Why Simultaneous equations cannot be greater than 2?

Thanks & Regards,
Prashant S Akerkar
Romsek is correct. You ask silly questions that you could research yourself. Please stop.
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May 31st, 2017, 10:01 AM   #5
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You can have any number of simultaneous equations.

A few points: if you have fewer equation than you do unknown terms, you cannot solve for specific values of those terms.

For example, the single equation x+ y= 2 has an infinite number "solutions", pairs of (x, y) that satisfy the equation: take any number for x and then y= 2- x gives an (x, y) solution.

The two equation x+ y+ z= 4, 2x+ y- z= 0 where there are two equations and three unknown terms have an infinite number of solutions.. If you subtract the first equation from the second, you get x+ 2z= -4. If z is any value at all, then x= -4- 2z and y= 4- x- z= 4+4z- z= 4+ 3z give (x, y, z) that satisfies the equation.

The three equations x+ y+ z+ u= 0, 3x- y+ z= 1, y- z- u= 0, with four unknown terms have an infinite number of solutions.

On the other hand, if you have more equations than unknown terms, you might have no solution at all. For example, the three equations x+ y= 2, x- 3y= -2, 2x+ y= 5 has no solution. The only numbers that satisfy x+ y= 2 and x- 3y= -2 are x= 1, y= 1 but they don't satisfy the last equation: 2(1)+ 1= 3 not 5.

If you have the same number of equations and unknown terms, say three equations and three unknown terms, there will be, generally, a unique solution. You do have to be careful that the equations are "independent". For example, the three equations x+ y+ z= 4, x- y+ z= 1, and 2x+ 2z= 5 are not independent- the last equation is just the sum of the first two. Any (x, y, z) that satisfy the first two (and, since that is two equations in three unknowns, there are an infinite number of solutions) will necessarily satisfy the third.
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May 31st, 2017, 10:05 AM   #6
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Quote:
Originally Posted by prashantakerkar View Post
Can there be more than two simultaneous
equations to be solved?

If yes, How many ? If Simultaneous equations > 2, How they can be simplified?

If No,Why Simultaneous equations cannot be greater than 2?

Thanks & Regards,
Prashant S Akerkar
Solved. Thank you for those serious thought-provoking, intellectually invigorating questions.
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May 31st, 2017, 11:13 AM   #7
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Thank you.

As you mentioned,there can be any finite number of Simultaneous equations, Can we also have any number of Simultaneous equations having complex numbers to be solved?

Thanks & Regards,
Prashant S Akerkar
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May 31st, 2017, 11:28 AM   #8
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Enough is enough.
He asked a perfectly sensible mathematical question.
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May 31st, 2017, 11:35 AM   #9
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He asked a perfectly sensible mathematical question.
It is and so it was answered several times, but the ratio of legitimate questions to total questions remains close to zero.

Moreover, and this is the real point, his legitimate questions are better answered by his doing a bit of research and learning something in context.
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May 31st, 2017, 11:45 AM   #10
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Originally Posted by prashantakerkar View Post
Thank you.

As you mentioned,there can be any finite number of Simultaneous equations, Can we also have any number of Simultaneous equations having complex numbers to be solved?

Thanks & Regards,
Prashant S Akerkar
Thank you for those serious thought-provoking, intellectually invigorating follow up questions.
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