## anonymous one year ago Fan and Medal Which of these equations are linear equations?

1. vikstar2.0

what are the equations

2. anonymous

$\frac{ x }{ 4 } - \frac{ y }{ 3 } = 1$

3. vikstar2.0

thats it or is there more

4. anonymous

there is more

5. anonymous

just wait im typing the equation

6. anonymous

$\frac{ 5 }{ x } - \frac{ 2 }{ y } = 7$

7. anonymous

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

8. vikstar2.0

@Hero @LynFran

9. anonymous

@vikstar2.0

10. vikstar2.0

i think it is both

11. anonymous

@Hero

12. vikstar2.0

but most likely the first one

13. anonymous

i need the work though

14. anonymous

Anybody who can help me????

15. anonymous

@ayeshaafzal221

16. anonymous

@SolomonZelman

17. vikstar2.0

how am i supposed to show the work?

18. anonymous

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

19. anonymous

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

20. anonymous

anyways could u pls explain

21. anonymous

@Hero

22. Hero

Try re writing both in linear form.

23. anonymous

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

24. Hero

.Please show the work you did to get that.

25. 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

26. anonymous

@Hero

27. anonymous

Where did @Hero go?

28. anonymous

Aw man, he's offline. :(

29. anonymous

@mathmate

30. anonymous

@dan815

31. anonymous

@pooja195

32. anonymous

@emily_wilson

33. anonymous

@SolomonZelman

34. pooja195

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

35. anonymous

I do not know. Do you want the options?

36. anonymous

@pooja195

37. anonymous

@Hero

38. anonymous

@Kate_J2002

39. Hero

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

40. anonymous

41. Hero

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

42. anonymous

Oh ok.

43. Hero

Multiply both sides of the equation by the LCD

44. anonymous

You mean the Least Common Denominator?

45. Hero

Exactly.

46. anonymous

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

47. anonymous

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

48. anonymous

I'm sorry for being so dumb.

49. anonymous

Are you there @Hero ?

50. anonymous

@pooja195

51. 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

52. anonymous

53. Hero

Correct.

54. anonymous

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

55. Hero

Correct

56. anonymous

Ok.

57. Hero

Don't forget to cross cancel where possible.

58. anonymous

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

59. Hero

Correct

60. Hero

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

61. anonymous

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

62. Hero

Now try writing the second equation In the same form.

63. anonymous

Ok just wait. Please don't leave.

64. anonymous

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

65. Hero

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

66. anonymous

x and y.

67. Hero

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

68. 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?

69. anonymous

Or am I wrong?

70. Hero

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

71. anonymous

Is it xy

72. Hero

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

73. Hero

Correct

74. anonymous

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

75. Hero

You have to SHOW that it isn't

76. anonymous

I don't actually know how to do that.

77. anonymous

78. Hero

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

79. anonymous

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

80. anonymous

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

81. Hero

Cross cancel

82. anonymous

What are those?

83. Hero

Factors of one that allow you to Simplify expressions.

84. anonymous

Oh ok.

85. Hero

Cross cancel

86. anonymous

So: 5xy - 3xy = 7xy

87. Hero

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

88. anonymous

:(

89. anonymous

How do I do that?

90. Hero

What does x/x =1 mean to you?

91. anonymous

1/1=1

92. Hero

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

93. anonymous

I'm confused.

94. 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

95. Hero

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

96. anonymous

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

97. Hero

For example, 7/7 =1 but 7 ≠1

98. anonymous

Ok.

99. 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.

100. Hero

So you should have ended up With:

101. Hero

5y-3x = 7xy

102. anonymous

oh ok

103. anonymous

Thank u very much @Hero ur the best.

104. Hero

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

105. anonymous

so it is not a linear equation

106. Hero

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

107. Hero

So, yes, correct, not linear.

108. anonymous

ok

109. anonymous

Thank u very much @Hero

110. Hero

yw