SOLUTION: Find the value of k for which the system of linear equations 2x+5y=3 ; (k+1)x+2(k+2)y=2k will have infinite number of solutions . ( Pls answer . .. Its urget ..........THAnkS

Question 32119: Find the value of k for which the system of linear equations 2x+5y=3 ; (k+1)x+2(k+2)y=2k will have infinite number of solutions . ( Pls answer . .. Its urget ..........THAnkS

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
For there to be an infinite number of solutions, the
equation (k+1)x+2(k+2)y=2k must be a multiple of
the equation 2x+5y=3
Let the multiplier by "a".
Then the equation is 2ax+5ay=3a
Then the following set of equation must be true:
k+1=2a
2k=3a
Then k=3a/2
Substitute that into k+1=2a to get:
(3a/2)+1=2a
(1/2)a=1
a=2
If a=2 then 2k=3(2) and k=3
Try It:
Substituting for "k" you get:
(3+1)x+2(3+2)y=2(3)
4x+10y=6
This is a multiple of the equation 2x+5y=3
Hope this helps.
Cheers,
Stan H.

RELATED QUESTIONS
Hi, I'm Michele and I could really use someones help on my problem. I will be greatful... (answered by stanbon)

what is k if the following system of equations has a unique solution: 2x+(k-1)y=6... (answered by stanbon)

Determine the value of k for which the system of linear equations 2x−y =5 6x+ky=2 (answered by MathLover1)

For which value of K the system of equations x+y=2 and x-y=K has an unique solution? (answered by ikleyn)

Find the value of k the system has infinite number of solution x+(k+1)y=5;(k+1)x+9y=8k-1 (answered by ikleyn,dubeypriyanshu436@gmail.com)

Find the Value of K K.......3+K.........-10 1-K......2-K......... 5 = 48 2... (answered by Edwin McCravy)

The value of K for which the system of linear equations 2x+y+2=0 X+ky+2z=0... (answered by Alan3354,KMST)

Find k if he following system of equations has a unique solution? 2x+(k-1)y=6... (answered by Edwin McCravy)

Help please.If k is a negative number, then which of the following equations will have... (answered by jim_thompson5910)