Math Is Fun Forum

Marisca

Member

Registered: 2011-04-22

Posts: 53

Linear literal equations

Hi, I'm having trouble solving for x with this question

1/(x+a) = b/x

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Linear literal equations

Hi Marisca

Multiply by x(x+1) throughout the equation,then get all terms with x in them to one side and all terms without x to the other side.Then you should have a standard linear equation.

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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: Linear literal equations

ok, so I'm not sure if this is right, but I got

x=-ab/(b-1)

also, why did you multiply by x(x+1)?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Linear literal equations

Hi Marisca

That's correct! The reason we multiply by x(x+1) is to get rid of x's in the denominator.

---

“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: Linear literal equations

Ok, thanks!

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Linear literal equations

If you have more question,please post them here

---

“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: Linear literal equations

Ok, I have another question.

x-y = 6 and 2x-2y=12 have infinitely many solutions. Describe these solutions through the use of a parameter.

All I've been able to do so far is set up the matrices, but I don't know where to go from there.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear literal equations

Hi Marisca;

Why do you need a parameter here? Can you not get every solution by

y = x - 6 ?

You can treat x as a parameter.

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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: Linear literal equations

hi Marisca

The matrix will have determinant zero so you won't get an inverse.

A parameter is just another variable so I think this question means

let x = k (say) be a possible value for x.  k is the parameter

Then in equation 1,    y = k - 6

Now try those 'values' in equation 2

LHS = 2x - 2y = 2k - 2(k - 6) = 2k - 2k --12 = +12 = RHS

So x = k,  y = k - 6 is a solution to this pair of equations for all values of k => infinitely many solutions.

Bob

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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

Marisca

Member

Registered: 2011-04-22

Posts: 53

Re: Linear literal equations

hi bobbym, the question was asking for a parameter.

Thanks, that really helped

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear literal equations

Hi Marisca;

You can use x as a parameter or change it to another letter or symbol.

---

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: Linear literal equations

Ok, thank you

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear literal equations

Your welcome!

---

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.