Fan and Medal
Which of these equations are linear equations?

- anonymous

Fan and Medal
Which of these equations are linear equations?

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- vikstar2.0

what are the equations

- anonymous

\[\frac{ x }{ 4 } - \frac{ y }{ 3 } = 1 \]

- vikstar2.0

thats it or is there more

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## More answers

- anonymous

there is more

- anonymous

just wait im typing the equation

- anonymous

\[\frac{ 5 }{ x } - \frac{ 2 }{ y } = 7\]

- anonymous

So is it:
a)the first one
b)the second one
c)or both

- vikstar2.0

@Hero @LynFran

- anonymous

@vikstar2.0

- vikstar2.0

i think it is both

- anonymous

@Hero

- vikstar2.0

but most likely the first one

- anonymous

i need the work though

- anonymous

Anybody who can help me????

- anonymous

@ayeshaafzal221

- anonymous

@SolomonZelman

- vikstar2.0

how am i supposed to show the work?

- anonymous

any equation in the form of y=mx+b is linear

- anonymous

i thought it was supposed to be ax+by=c

- anonymous

anyways could u pls explain

- anonymous

@Hero

- Hero

Try re writing both in linear form.

- anonymous

For the first one, I think it is 3x-4y=12, but I'm still not that sure how I got 12.

- Hero

.Please show the work you did to get that.

- anonymous

I cross-multiplied:
3(x) and 4(y), which gave me 3x-4y. And then I guess I multiplied the 3 and 4 and got 12.
So 3x-4y=12

- anonymous

@Hero

- anonymous

Where did @Hero go?

- anonymous

Aw man, he's offline. :(

- anonymous

@mathmate

- anonymous

@dan815

- anonymous

@pooja195

- anonymous

@emily_wilson

- anonymous

@SolomonZelman

- pooja195

Is there a way you can post the questions and options in one post?

- anonymous

I do not know. Do you want the options?

- anonymous

@pooja195

- anonymous

@Hero

- anonymous

@Kate_J2002

- Hero

The approach you took is not "algebraic" and would be considered an incorrect approach.

- anonymous

Oh sorry could you please help me to do it the correct way?

- Hero

You don't cross multiply The difference of two fractions.

- anonymous

Oh ok.

- Hero

Multiply both sides of the equation by the LCD

- anonymous

You mean the Least Common Denominator?

- Hero

Exactly.

- anonymous

Ok let me try. Don't leave, please.

- anonymous

But there are 2 fractions on one side of the equation, so how will I find the LCD?

- anonymous

I'm sorry for being so dumb.

- anonymous

Are you there @Hero ?

- anonymous

@pooja195

- Hero

I'M here. The LCD is twelve. you should watch a tutorial on how to find the LCD of two fractions going forward though

- anonymous

Your talking about the first equation, right?

- Hero

Correct.

- anonymous

Ok so I should multiply 12 with both the fractions and 1, right?

- Hero

Correct

- anonymous

Ok.

- Hero

Don't forget to cross cancel where possible.

- anonymous

So:
12x/4 - 12y/3 = 12
3x - 4y = 12

- Hero

Correct

- Hero

So you know the first equation is linear since it has the general linear form.

- anonymous

OK NOW I GET IT! Isn't 3x - 4y = 12 a linear equation in standard form, which is
ax - by = c

- Hero

Now try writing the second equation In the same form.

- anonymous

Ok just wait. Please don't leave.

- anonymous

So 10 is the LCD for the second equation, right?

- Hero

Tell me what is in the denominators of the fractions of the Second equation?

- anonymous

x and y.

- Hero

Explain how 10 Can be the LCD of x and y.

- anonymous

OH WAIT SO YOU CANNOT FIND THE LCD FOR THE SECOND EQUATION BECAUSE THEY'RE VARIABLES. So that means it is NOT A LINEAR EQUATION, right?

- anonymous

Or am I wrong?

- Hero

Actually, there IS an LCD for denominators x and y.

- anonymous

Is it xy

- Hero

You find it the same way you found the LCD of 3 and 4

- Hero

Correct

- anonymous

Yay! But the second equation isn't a linear equation, right?

- Hero

You have to SHOW that it isn't

- anonymous

I don't actually know how to do that.

- anonymous

Please help me out.

- Hero

Try to write it in linear form. You already found the LCD. Remember what to do afterwards?

- anonymous

OH YEAH! Just give a minute. I'll solve it out. Just stay there.

- anonymous

So:
5xy/1x - 3xy/1y = 7xy

- Hero

Cross cancel

- anonymous

What are those?

- Hero

Factors of one that allow you to Simplify expressions.

- anonymous

Oh ok.

- Hero

Cross cancel

- anonymous

So:
5xy - 3xy = 7xy

- Hero

You have good intention but that is not the correct Simplification.

- anonymous

:(

- anonymous

How do I do that?

- Hero

What does x/x =1 mean to you?

- anonymous

1/1=1

- Hero

Well that would imply that x=1 but x is a variable

- anonymous

I'm confused.

- Hero

Basically for any fraction, if you have a factor in the numerator and the same factor in the denominator of a fraction, then the factors cancel to just 1

- Hero

The factors together Cancel to get 1 but a factor by itself does not equal one.

- anonymous

Oh ok but I don't know where this going.

- Hero

For example, 7/7 =1 but 7 ≠1

- anonymous

Ok.

- Hero

The way it's going is I can cancel any factor that occurs in both the numerator and denominator Without changing the value of the fraction.

- Hero

So you should have ended up With:

- Hero

5y-3x = 7xy

- anonymous

oh ok

- anonymous

Thank u very much @Hero ur the best.

- Hero

Which can also be written as -3x + 5y = 7xy

- anonymous

so it is not a linear equation

- Hero

But it is NOT Linear because 7xy is clearly not a constant,

- Hero

So, yes, correct, not linear.

- anonymous

ok

- anonymous

Thank u very much @Hero

- Hero

yw

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