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

1. mayankdevnani Group Title

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

2. hartnn Group Title

i think there is easier way out....

3. ash2326 Group Title

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 Group Title

^^ exactly

5. ParthKohli Group Title

@hartnn: Oh yeah

6. sauravshakya Group Title

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

7. hartnn Group Title

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

8. ParthKohli Group Title

Yes.

9. mayankdevnani Group Title

@ash2326 gd and then

10. Zarkon Group Title

and why would that have an infinite # of solutions?

11. hartnn Group Title

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

12. Zarkon Group Title

ash2326's solution is mostly correct

13. Zarkon Group Title

this one doesn't satisfy that

14. mayankdevnani Group Title

ok! then @Zarkon

15. Zarkon Group Title

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

16. mayankdevnani Group Title

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

17. Zarkon Group Title

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 Group Title

thus no solution

19. mayankdevnani Group Title

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

20. mayankdevnani Group Title

and then solve it

21. mathslover Group Title

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 Group Title

@mayankdevnani what r u doing?

23. mathslover Group Title

@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 Group Title

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

25. mathslover Group Title

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

26. mayankdevnani Group Title

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

27. mathslover Group Title

@mayankdevnani where are you not getting ?

28. mayankdevnani Group Title

step by step

29. sauravshakya Group Title

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

30. Zarkon Group Title

31. mathslover Group Title

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

32. mathslover Group Title

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

33. mayankdevnani Group Title

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

34. ghazi Group Title

-4/3

35. mayankdevnani Group Title

ya.. but how??

36. ghazi Group Title

that will be a prallal line

37. mathslover Group Title

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 Group Title

got it @mayankdevnani ?

39. ghazi Group Title

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 Group Title

@mayankdevnani clear?

41. mayankdevnani Group Title

ok... @mathslover

42. ghazi Group Title

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

43. ghazi Group Title

neither do they overlap

44. mayankdevnani Group Title

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

45. ghazi Group Title

:)

46. ghazi Group Title

@mathslover is my approach correct?

47. sauravshakya Group Title

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

48. ghazi Group Title

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 Group Title

yes it is similar to that of @ash2326