Question

Find out \(x\) and \(y\) :- \(3\dfrac{7}{x} \times y\dfrac{3}{15}=8\)

Answer 1

Diophantine equation?

Answer 2

o_O

Answer 3

\[\dfrac{3x + 7}{x} + \dfrac{5y + 1}{5} = 8\]

Answer 4

Diophantine equation=?

It's the question of N.T.S.E algebra, i don't know nothing more than this

Answer 5

Do you need just the integer solutions?

Answer 6

\[\frac{15x+35+5yx+x}{5x}=8\]\[16x+35+5yx=40x\]\[35+5yx=24x\]& yes @ParthKohli i only need an integer solution :)

Answer 7

Hmm... complete the square?

Answer 8

35 = (24 - 5y)x
try factorizing 35

Answer 9

3 + 7/x + y+1/5 =8
7/x + y = 24/5
7/x = (24-5y)/5
So,
x=5n
and 7=(24-5y)n
y=4 + (4n-7)/5n

Answer 10

Since 5n>4n-7 for n>0
No positive integer solution

Answer 11

ans. 11, 2

Answer 12

looks like you didn't do the algebra correctly ..
http://www.wolframalpha.com/input/?i=integer+solution+35%2B5yx%3D24x

Answer 13

Hey! parth i found a page on diophantine equations

Answer 14

Yes! @experimentX I was searching for the factoring trick =)

Answer 15

this is a classic trick
35 = 1x35
35 = 7x5
--------------
1*35 = x * (5y - 24)
compare these types of factors and see if you get integer values.

just an example :)

Answer 16

@jiteshmeghwal9 Search for Art of Problem Solving's video: Simon's Favorite Factoring Trick

Answer 17

Then is the answer given in my book is wrong ?

Answer 18

no ... what i copied was erroneous data

Answer 19

ohh..k

Answer 20

hah!! how could this yield same result
http://www.wolframalpha.com/input/?i=integer+solution+7%2Fx+%3D+%2824-5y%29%2F5

Answer 21

perhaps the algebra was right and the answer on book is wrong.

Answer 22

(3 + 7/x) (y +3/15) =8
(y+3/15) = 8/(3 +7/x)
(15y+3)/15 = 8x/(3x+7)
=> 8x =(15y+3)n
=>(3x+7)=15n

Answer 23

even the solution is pretty clear from this equation
7 (24-5y)
-- = --------
x 5

Answer 24

24-5y=7
5y=17
y=17/5

x=5

Answer 25

Is this the right answer ?

Answer 26

@experimentX ?

Answer 27

But \(17/5\) is not an integer :P

Answer 28

woops!! sorry ... i guess I made error there. Let me check again. Don't have much time.

Answer 29

3 + 7/x + y +1/5 =8
(3x+7)/x = 8 - y - 1/5
--------------------
\[ \frac{3x+7}{x} = \frac{5(8-y)-1 }{5} \]

Answer 30

multiply both by 'k' ... numerator and denominator, and look for integer values.
x = 5k
15k + 7 = 5(8-y)-1

Answer 31

the original problem is \[3\frac{7}{x}\times y\frac{3}{15}=8\] but your beginning line is \[3\frac{7}{x}\color{red} + y\frac{3}{15}=8\] so you probably will not get \(x=11,y=2\)

Answer 32

I'm totally confused

Answer 33

LOL, @sirm3d u wrote we'll \(\LARGE\star not\) get x=11, y=2, haha :)

Answer 34

(3 + 7/x) (y +3/15) =8
(y+3/15) = 8/(3 +7/x)
(15y+3)/15 = 8x/(3x+7)
=> 8x =(15y+3)n
=>(3x+7)=15n

Answer 35

I guess NO SOLUTION

Answer 36

Everyone has their own opinion, what's the real answer ???

Answer 37

i found the solution \(11,\;y=2\)

Answer 38

x =(7y+21)/(111-3y)

Answer 39

7(y+3)/3(37-y)

Answer 40

If solution exists 7y+21>=111-3y
=>y>=9

Answer 41

\[\vdots\\(3x+7)(25y+1)=40x\\40x=(1,40x),(2,20x),\dots (40,x);(x,40),(2x,20),\dots,(40x,1)\]

Answer 42

typo error above. it should be \(5y+1\)
by choosing \((40,x)\) as factors of 40,
\[3x+7=40,\;5y+1=x\]

Answer 43

x=21,y=40 is a solution for the problem as initially stated

Answer 44

\[3x+7=40\Rightarrow x=11\\5y+1=x=11\Rightarrow y=2\]

Answer 45

(3 +7/x) (y+3/15) =8
.
.
.
y=(31x+21)/(15x+35)
y=(30x+70+x-49)/(15x+35)
y=2 + (x-49)/(15x+35)

Answer 46

when x=-6
y = 2 + (-6-49) / (15 *(-6) +35)
y=3

Answer 47

So, x=-6 and y=3

Answer 48

Now,
Since I15x+35I > Ix-49I for x<=-7 and x>=1
x cannot be l than and equal to -7 and cannot be greater than 1

Answer 49

And NO SOLUTION in the interval -5<=x<=0

Answer 50

So, If I did my algebra correct the only solution is x=-6 and y=3

Answer 51

And which equation do you find x=-6 and y = 3 to solve?

Answer 52

Achcha toh upar waali equation ko simplify karke kya nikalta hai?

Answer 53

35+5yx=24x

Answer 54

Toh hum diophantine equations mein factorization kar sakte hain jinka form hai \(axy + bx + cy =0\) ya phir \(axy + bx + c\) ya phir \(axy + by + c\).

Answer 55

Trick hai ki humein woh constant ko ek side laana hai aur left side factor karna hai

Answer 56

accha thik hai toh equation 35+5yx-24x=0 mein change ho jaayegi

Answer 57

Ab equation mein -1 multiply karo aur 35 dusri side le jao

Answer 58

pehle -1 multiplly karu yaa 35 dudri side le jaaun ?

Answer 59

Kuch bhi kar lo yaar!

Answer 60

-1(35+5yx-24x)=0
-35-5yx+24x=0
-5yx+24x=35

Answer 61

haan, LHS factor karo

Answer 62

-x(5y-24)

Answer 63

Yes, ab dhyan se dekho:\[35 = 1\times 35 \\ 35 = 7\times 5 \\ 35 = 5\times 7 \\ 35 = 35\times 1 \]

Answer 64

Toh dekho, hum dekh sakte hain ki \(-x\) aur \(5y - 24\) ka product \(35\) hai, right?

Answer 65

yes!

Answer 66

Par jo maine upar post kiya, jaise \(1,35\) aur \(7,5\) etc., unka bhi toh product \(35\) hai na!

Answer 67

haan

Answer 68

Matlab ki humara solution inmein se ek equations se niklega:\[-x = 1, \ \ 5y - 24 =35 \\ -x = 7, \ 5y-24 =5 \\ -x = 5, \ 5y - 24 = 7 \\ -x = 35, 5y - 24 = 1\]

Answer 69

Jis bhi equation mein dono \(x\) aur \(y\) integer ho, wohi answer hai!

Answer 70

4th equation :- x=-35
y=5

Answer 71

Yes =) ab answer check karo

Answer 72

book ke answer se toh yeh match nahi kar raha hai

Answer 73

Arrey book ko chhodo, book khoosat hoti hain ;)

Answer 74

haha, ok i gt it, thanx :)

Answer 75

You're welcome ^_^