## mariomintchev 3 years ago 5x+5y=1 25x+ky=4 solve for k

1. Kuoministers

there is few ways of working this out. Elimination, Substitution and maybe multiplication

2. Kuoministers

which way do you prefer?

3. mariomintchev

i need my mind refreshed. whichever method works best is the method i choose.

4. Kuoministers

ill use substitution then :P x = $x = y - \frac{ 1 }{ 5 }$ 25x + ky = 4

5. Kuoministers

25(y - $25(y - \frac{ 1 }{ 5 }) + ky = 4$

6. Kuoministers

$25y - 5 + ky = 4$

7. Kuoministers

do you get it now?

8. mariomintchev

howd u get y-(1/5)?

9. Kuoministers

divide everything in the first equation by 5

10. Kuoministers

there is no solution :)

11. Kuoministers

ill use elimination now

12. Kuoministers

times the first equation by -5 -25x - 25y = -5 25x + ky = 4

13. Kuoministers

now add this equation vertically together. it would give you k=25

14. mariomintchev

i probably shoulda phrased the question the way they have it on my hw. it says: Determine the value of k for which the system of linear equations has no solutions.

15. Kuoministers

haha great :/ u say that now

16. Kuoministers

you know why there is no solution? if you sub K = 25 it wont work

17. mariomintchev

:(

18. mariomintchev

yes?

19. mariomintchev

because they equal different things

20. Kuoministers

$\Huge{\color{Purple}{\\{\ \boxed{\mathbb{\text{}{}}{\color{green}{\color{blue}T{\color{purple}h{\color{pink}a{\color{red}nk}}}}}}}}}$ $\Huge{\color{Purple}{\\{\ \boxed{\mathbb{\text{}{}}{\color{blue}Y{\color{green}o{\color{red}u}}}}}}}$

21. mariomintchev

haha no, THANK YOU ! :)

22. mariomintchev

ok i have another one lol this one wants the k to have an infinite amount of solutions

23. mariomintchev

49x-49y=49 7x+ky=7

24. mariomintchev

the answer is not 1,7,49,1/7, or 1/49.

25. mariomintchev

@Kuoministers

26. Kuoministers

sorry been bit busy

27. Kuoministers

so do you have an idea where to start?

28. Kuoministers

i would times the 2nd equation by 7

29. mariomintchev

ok...

30. Kuoministers

do you undertand this yet lol?

31. Kuoministers

49x-49y=49 7x+ky=7 49x-49y=49 49x + 7ky = 49

32. mariomintchev

dont know where to go from there

33. Kuoministers

-49y - 7ky = 0 -7y(7 + k) = 0

34. mariomintchev

how do we get the k from that

35. Kuoministers

im bit confused :P you sure their is more than 1 answer??

36. mariomintchev

37. Kuoministers

oh u said this one wants the k to have an infinite amount of solutions

38. mariomintchev

1 K but infinite solutions we need the K

39. Kuoministers

y(7 + k ) = 0 from this can you find K? im pretty sure you can :P

40. Kuoministers

hint: you only need to look at this question to get K

41. mariomintchev

ok its -7 lol

42. mariomintchev

im feeling slooow ha

43. Kuoministers

ok i g2g now :)

44. Kuoministers