Question

Find the value of k for which the pair of equations 4x-5y=5 and kx+3y=3 is consistent.

Answer 1

for consistent,two cases arise
(1) for unique solution
a1/a2 not equal to b1/b2
4/k not equal to-5/3
k not equal to -12/5...(A)
(2) for infinitely many solutions
a1/a2 = b1/b2=c1/c2
4/k=-5/3=5/3
k=-12/5 or k=12/5....(B)
from (A) &(B)
k=12/5

Answer 2

Answer:

Value of k is 12/5

Step-by-step explanation:

4x-5y=5.....(i) and kx+3y=3 .....(ii) are two equations

Comparing (i) and (ii) with a₁x + b₁x + c₁ = 0 and a₂x + b₂x + c₂ = 0 respectively

Here a₁ = 4,b₁ = 5,c₁ =− 5 anda₂ = k,b₂ = 3,c₂ =− 3

Now given equations are consistent,

So here two cases will arise

First case,

For unique solution,

a₁/a₂is not equal to b₁/b₂

So, 4/k is nlt equal to -5/3

K is nkt equal to -12/5.......(i)

Second case,

For infinitely solution,

a₁/a₂ = b₁/b₂ = c₁/c₂

So,4/k=-5/3=5/3

K= -12/5 or k= 12/5.....(ii)

From equations (i) and (ii)

k=12/5