Fan and Medal Which of these equations are linear equations?

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Fan and Medal Which of these equations are linear equations?

Mathematics
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what are the equations
\[\frac{ x }{ 4 } - \frac{ y }{ 3 } = 1 \]
thats it or is there more

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Other answers:

there is more
just wait im typing the equation
\[\frac{ 5 }{ x } - \frac{ 2 }{ y } = 7\]
So is it: a)the first one b)the second one c)or both
i think it is both
but most likely the first one
i need the work though
Anybody who can help me????
how am i supposed to show the work?
any equation in the form of y=mx+b is linear
i thought it was supposed to be ax+by=c
anyways could u pls explain
Try re writing both in linear form.
For the first one, I think it is 3x-4y=12, but I'm still not that sure how I got 12.
.Please show the work you did to get that.
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
Where did @Hero go?
Aw man, he's offline. :(
Is there a way you can post the questions and options in one post?
I do not know. Do you want the options?
The approach you took is not "algebraic" and would be considered an incorrect approach.
Oh sorry could you please help me to do it the correct way?
You don't cross multiply The difference of two fractions.
Oh ok.
Multiply both sides of the equation by the LCD
You mean the Least Common Denominator?
Exactly.
Ok let me try. Don't leave, please.
But there are 2 fractions on one side of the equation, so how will I find the LCD?
I'm sorry for being so dumb.
Are you there @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
Your talking about the first equation, right?
Correct.
Ok so I should multiply 12 with both the fractions and 1, right?
Correct
Ok.
Don't forget to cross cancel where possible.
So: 12x/4 - 12y/3 = 12 3x - 4y = 12
Correct
So you know the first equation is linear since it has the general linear form.
OK NOW I GET IT! Isn't 3x - 4y = 12 a linear equation in standard form, which is ax - by = c
Now try writing the second equation In the same form.
Ok just wait. Please don't leave.
So 10 is the LCD for the second equation, right?
Tell me what is in the denominators of the fractions of the Second equation?
x and y.
Explain how 10 Can be the LCD of x and y.
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?
Or am I wrong?
Actually, there IS an LCD for denominators x and y.
Is it xy
You find it the same way you found the LCD of 3 and 4
Correct
Yay! But the second equation isn't a linear equation, right?
You have to SHOW that it isn't
I don't actually know how to do that.
Please help me out.
Try to write it in linear form. You already found the LCD. Remember what to do afterwards?
OH YEAH! Just give a minute. I'll solve it out. Just stay there.
So: 5xy/1x - 3xy/1y = 7xy
Cross cancel
What are those?
Factors of one that allow you to Simplify expressions.
Oh ok.
Cross cancel
So: 5xy - 3xy = 7xy
You have good intention but that is not the correct Simplification.
:(
How do I do that?
What does x/x =1 mean to you?
1/1=1
Well that would imply that x=1 but x is a variable
I'm confused.
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
The factors together Cancel to get 1 but a factor by itself does not equal one.
Oh ok but I don't know where this going.
For example, 7/7 =1 but 7 ≠1
Ok.
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.
So you should have ended up With:
5y-3x = 7xy
oh ok
Thank u very much @Hero ur the best.
Which can also be written as -3x + 5y = 7xy
so it is not a linear equation
But it is NOT Linear because 7xy is clearly not a constant,
So, yes, correct, not linear.
ok
Thank u very much @Hero
yw

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