SOLUTION: 5(x+999) = -7(y+23322) (2k+1)(y+23322) = k(x+999) I just need to know which value of "k" will make the equation have infinitely many solutions. Can someone give me a step by step

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 5(x+999) = -7(y+23322) (2k+1)(y+23322) = k(x+999) I just need to know which value of "k" will make the equation have infinitely many solutions. Can someone give me a step by step      Log On


   

Question 1131389: 5(x+999) = -7(y+23322)
(2k+1)(y+23322) = k(x+999)
I just need to know which value of "k" will make the equation have infinitely many solutions. Can someone give me a step by step because I am lost here. Thank you!
Found 2 solutions by JoelSchwartz, greenestamps:
Answer by JoelSchwartz(130) About Me  (Show Source):
You can put this solution on YOUR website!
5(x+999)=-7(y+23322)
(x+999)=(-7(y+23322))/5
((x+999))/(y+23322)=-7/5
(2k+1)(y+23322)=k(x+999)
(2k+1)=k(x+999)/(y+23322)
2k+1=k*-7/5
10k+5=-7k
17k=-5
k=-5/17

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Solve each equation for (y+22332)/(x+999):

(1) 5%28x%2B999%29+=+-7%28y%2B23322%29 --> %28y%2B22332%29%2F%28x%2B999%29+=+-5%2F7
(2) %282k%2B1%29%28y%2B23322%29+=+k%28x%2B999%29 --> %28y%2B22332%29%2F%28x%2B999%29+=+k%2F%282k%2B1%29

So

-5%2F7+=+k%2F%282k%2B1%29
7k+=+-10k-5
17k+=+-5
k+=+-5%2F17