# find the value of k

#### 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

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.

Last edited:

#### undefined

MHF Hall of Honor
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

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...

• mr fantastic

#### saha.subham

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

#### undefined

MHF Hall of Honor
i no the process but just getting stuck in factorising so plzz anybody help me
Factorising???

Write

$$\displaystyle \frac{k-1}{k+1}=\frac{-1}{1-k}=\frac{5}{3k+1}$$

and solve for $$\displaystyle k$$.

#### saha.subham

Factorising???

Write

$$\displaystyle \frac{k-1}{k+1}=\frac{-1}{1-k}=\frac{5}{3k+1}$$

and solve for $$\displaystyle k$$.
forget abt it plzz solve it fully

#### HallsofIvy

MHF Helper
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?

• FlacidCelery and mr fantastic

#### saha.subham

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

#### undefined

MHF Hall of Honor
i have solved all this type of sums accept 3 this is one of them plzz help
In what I wrote above, we have

$$\displaystyle \frac{-1}{1-k}=\frac{5}{3k+1}$$

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

#### saha.subham

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.

#### saha.subham

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.