Thread: find the value of k

find the value of k such that the system has infinite number of solutions


(k-1)x - y = 5
(k+1)x + (1-k)y = (3k+1)

plzz solve it wholly

thnks in advance

i am aquinted with the process of taking 3 cases and show the common value of k in all is the answer. so it will be helpful if u solve it with this process. i am having problem with factorising so plzz solve it wholly.

Originally Posted by saha.subham

find the value of k such that the system has infinite number of solutions


(k-1)x - y = 5
(k+1)x + (1-k)y = (3k+1)

plzz solve it wholly

thnks in advance

i am aquinted with the process of taking 3 cases and show the common value of k in all is the answer. so it will be helpful if u solve it with this process. i am having problem with factorising so plzz solve it wholly.

Someone will probably post a full solution after me, but I prefer to give a hint.

Consider the equations

x = y + 1
2x = 2y + 2

Note how this system has an infinite number of solutions.

So...

i no the process but just getting stuck in factorising so plzz anybody help me

Originally Posted by saha.subham

i no the process but just getting stuck in factorising so plzz anybody help me

Factorising???

Write



and solve for .

Originally Posted by undefined

Factorising???

Write



and solve for .

forget abt it plzz solve it fully

Have you even tried anything yourself? In particular, in the original system,
(k-1)x - y = 5
(k+1)x + (1-k)y = (3k+1)
if you multiply the first equation by 1- k and add to the second equation, what do you get?

i have solved all this type of sums accept 3 this is one of them plzz help

Originally Posted by saha.subham

i have solved all this type of sums accept 3 this is one of them plzz help

In what I wrote above, we have



Solve for .. cross multiply.. easy stuff... plug the value you get back into the equations and see that it works out very nicely..

i understands it but i want to do all the sums by the same process
my process is
case1 -
for terms 1 and 2 i have to show the value of k

case 2

for terms 2 and 3 i have to show the value of k

case 3

for terms 1 and 3 i have to show the value of k

now the common value of k in all is the answer.

i have solved for case 2

for case 1 i have
k-1/k+1 = -1/1-k

for case 3

k-1/k+1 = 5/3k+1


plzz solve for k in both the case which i am not being able to do.

Hi saha.subham,

If then

ad = bc.

Similarly, can you simplify

=

Ah, it wasn't clear to me that you knew how to write the equations but not solve them. I did not know that the three cases you mentioned were the ones I wrote down. Please try to be a little more specific in the future, and show work; you would have gotten the guidance you needed a lot sooner that way.

I figured since solving systems of equations is more advanced than cross multiplying that you knew the procedure. Hopefully with sa-ri-ga-ma's post you will now have what you require to complete the problem.

Best regards.

Edit: Maybe by "factorising" you meant applying the distributive property? For example if you wanted to solve



you would need to distribute as follows





Or further on, there is a place to factor out a .







Of course it's much easier to just solve



and plug in the value of you find to make sure it satisfies



Anyway, this is a complete solution to one of the three cases you mentioned, so now you really should have all the tools you need to solve the other cases.