Question

Fan and Medal
Which of these equations are linear equations?

Answer 1

what are the equations

Answer 2

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

Answer 3

thats it or is there more

Answer 4

there is more

Answer 5

just wait im typing the equation

Answer 6

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

Answer 7

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

Answer 8

@Hero @LynFran

Answer 9

@vikstar2.0

Answer 10

i think it is both

Answer 11

@Hero

Answer 12

but most likely the first one

Answer 13

i need the work though

Answer 14

Anybody who can help me????

Answer 15

@ayeshaafzal221

Answer 16

@SolomonZelman

Answer 17

how am i supposed to show the work?

Answer 18

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

Answer 19

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

Answer 20

anyways could u pls explain

Answer 21

@Hero

Answer 22

Try re writing both in linear form.

Answer 23

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

Answer 24

.Please show the work you did to get that.

Answer 25

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

Answer 26

@Hero

Answer 27

Where did @Hero go?

Answer 28

Aw man, he's offline. :(

Answer 29

@mathmate

Answer 30

@dan815

Answer 31

@pooja195

Answer 32

@emily_wilson

Answer 33

@SolomonZelman

Answer 34

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

Answer 35

I do not know. Do you want the options?

Answer 36

@pooja195

Answer 37

@Hero

Answer 38

@Kate_J2002

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

Oh ok.

Answer 43

Multiply both sides of the equation by the LCD

Answer 44

You mean the Least Common Denominator?

Answer 45

Exactly.

Answer 46

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

Answer 47

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

Answer 48

I'm sorry for being so dumb.

Answer 49

Are you there @Hero ?

Answer 50

@pooja195

Answer 51

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

Answer 52

Your talking about the first equation, right?

Answer 53

Correct.

Answer 54

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

Answer 55

Correct

Answer 56

Ok.

Answer 57

Don't forget to cross cancel where possible.

Answer 58

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

Answer 59

Correct

Answer 60

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

Answer 61

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

Answer 62

Now try writing the second equation In the same form.

Answer 63

Ok just wait. Please don't leave.

Answer 64

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

Answer 65

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

Answer 66

x and y.

Answer 67

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

Answer 68

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?

Answer 69

Or am I wrong?

Answer 70

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

Answer 71

Is it xy

Answer 72

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

Answer 73

Correct

Answer 74

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

Answer 75

You have to SHOW that it isn't

Answer 76

I don't actually know how to do that.

Answer 77

Please help me out.

Answer 78

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

Answer 79

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

Answer 80

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

Answer 81

Cross cancel

Answer 82

What are those?

Answer 83

Factors of one that allow you to Simplify expressions.

Answer 84

Oh ok.

Answer 85

Cross cancel

Answer 86

So:
5xy - 3xy = 7xy

Answer 87

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

Answer 88

:(

Answer 89

How do I do that?

Answer 90

What does x/x =1 mean to you?

Answer 91

1/1=1

Answer 92

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

Answer 93

I'm confused.

Answer 94

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

Answer 95

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

Answer 96

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