## mayankdevnani 3 years ago Given: 3x-4y=7 and x+cy=13 , for what value of "c" will the two equations not have a solution?

1. mayankdevnani

options are : a) $\frac{3}{4}$ b)$\frac{4}{3}$ c) $-4$ d) $\frac{-4}{3}$

2. hartnn

i think there is easier way out....

3. ash2326

Rewrite first equation $x-\frac{4}{3}y=7$ for no solution we need to have parallel lines second equation $x+cy=13$ compare this with the first $c=-\frac{4}{3}$

4. hartnn

^^ exactly

5. ParthKohli

@hartnn: Oh yeah

6. sauravshakya

WELL FOLLOW @ash2326 THAT ONE MUCH EASIER..... agreed with @hartnn

7. hartnn

no solution is of the form: ax+b=c ax+b=d

8. ParthKohli

Yes.

9. mayankdevnani

@ash2326 gd and then

10. Zarkon

and why would that have an infinite # of solutions?

11. hartnn

because ax+b=c and ax+b=c are satisfied by infinite number of points (x,y) simultaneously.

12. Zarkon

ash2326's solution is mostly correct

13. Zarkon

this one doesn't satisfy that

14. mayankdevnani

ok! then @Zarkon

15. Zarkon

3x-4y=7 and x+cy=13 $x-\frac{4}{3}y=\frac{7}{3}$ $x+cy=13$

16. mayankdevnani

yaa ... i also agree with @Zarkon don't you @mathslover

17. Zarkon

if c=-4/3 then you get $x-\frac{4}{3}y=\frac{7}{3}$ and $x-\frac{4}{3}y=13$ ie $\frac{7}{3}=13$

18. Zarkon

thus no solution

19. mayankdevnani

isn't like this $3x-4y=7$ $3x=7-4y$ $x-y=\frac{7}{12}$ $x=\frac{7}{12}+y$

20. mayankdevnani

and then solve it

21. mathslover

What I did is this : $\large{7+4y = 3(13-cy)}$ $\large{7+4y=39-3cy}$ $\large{32= 4y+3cy}$ We have to find the value of c when the RHS becomes zero which will give no solution. $\large{4y+3(c)(y)=0}$ $\large{c = \frac{-4y}{3y}}$ $\large{c=\frac{-4}{3}}$ hence at c = -4/3 we get no solutions for the variables in the given two equations .

22. sauravshakya

@mayankdevnani what r u doing?

23. mathslover

@mayankdevnani you need to concentrate hardly on understanding questions... You are solving for x or y but in the question we have to find the value for c which makes the solutions for the equation as null set.

24. mayankdevnani

how did you get it......... @mathslover

25. mathslover

btw , @Zarkon sir , was my method acceptable? I know there are easy methods too.. but that is what I did..

26. mayankdevnani

ANSWER is correct... but i did'nt understand..... plz tell me once again.....

27. mathslover

@mayankdevnani where are you not getting ?

28. mayankdevnani

step by step

29. sauravshakya

THAT WAS exactly what I was thinking @mathslover THAT IS ABSOULETLY CORRECT

30. Zarkon

31. mathslover

OK thanks @sauravshakya Let us wait for honorable zarkon sir ..

32. mathslover

OK thanks a lot @Zarkon .. that fine made a lot sense sir.. :)

33. mayankdevnani

@mathslover how did you get it $7+4y=1(13-cy)$

34. ghazi

-4/3

35. mayankdevnani

ya.. but how??

36. ghazi

that will be a prallal line

37. mathslover

3x-4y = 7 x = (7+4y) / 3 and then : x + cy = 13 x = 13-cy 13-cy = (7+4y)/3 (since they are equal to x) 3(13-cy) = 7+4y

38. mathslover

got it @mayankdevnani ?

39. ghazi

just put -4/3 at C and you will have a parallel set of line and parallel set of lines have no solution

40. ghazi

@mayankdevnani clear?

41. mayankdevnani

ok... @mathslover

42. ghazi

3x-4y=7 and 3x-4y=39 are parallel lines how could they have a solution ..they intersect nowhere

43. ghazi

neither do they overlap

44. mayankdevnani

thnx.... @Zarkon @ghazi @sauravshakya @ash2326 but special thnx to @mathslover

45. ghazi

:)

46. ghazi

@mathslover is my approach correct?

47. sauravshakya

Isnt your method same as @ash2326 's method........ @ghazi

48. ghazi

i didn't see ...i just came here read the question and identified these are parallel lines...i guess yes both have same solution and we don't need to solve anything because already it is visible that it's case of parallel line when c= -4/3 hence no solution

49. ghazi

yes it is similar to that of @ash2326