Math Is Fun Forum

Marisca

Member

Registered: 2011-04-22

Posts: 53

Unique, infinite and no solutions...

Hi, could anyone help me with this problem?

Find the values of b and c, or the relationship  between b and c, for which the equations
x+5y=4 and 2x+by=c have:
I) a unique solution,
II) an infinite set of equations,
III) no solution.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Unique, infinite and no solutions...

Hi;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Unique, infinite and no solutions...

hi

Last edited by anonimnystefy (2012-01-14 02:04:16)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Marisca

Member

Registered: 2011-04-22

Posts: 53

Re: Unique, infinite and no solutions...

Thanks, but I don't understand how you arrived at those answers.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Unique, infinite and no solutions...

Hi Marisca;

Mine is easy it is on top of the original line therefore it has an infinte number of solutions.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Marisca

Member

Registered: 2011-04-22

Posts: 53

Re: Unique, infinite and no solutions...

Thanks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Unique, infinite and no solutions...

Hi;

Please look here for a complete description:

http://www.mathsisfun.com/algebra/syste … tions.html

You might like this too:

http://www.mathwarehouse.com/algebra/li … /index.php

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Unique, infinite and no solutions...

hi Marisca,

I've only just spotted your question.  The graph below may help you to understand why the three possibilities can apply.

Equations of this format are called 'linear equations' because you can work out some x and y values and plot them on a graph.

The result will be a straight line. 

The line x + 5y = 4 is fixed.  It goes through (4,0) and (-1,1).

The other line, 2x + by = c , will vary as you change b and c.

I've shown it crossing the first line.  That will always happen (I) unless the lines have the same gradient.

The same gradient will occur when b/2 = 5/1 => b = 10.

In such a case the lines will be parallel so will never cross (III), unless they are the same line.

If b = 10 and c = 8, they will be the same line and so 'cross' everywhere along their length (II).

Bob

Last edited by Bob (2012-01-14 23:42:20)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob