Question

find the value of k for which the following pair of equations has no solution X + 2 Y is equals to 3 ,(k-1)X +(k+1)y=(k+2)​

Answer 1

Answer:

k ≠ 3

Step-by-step explanation:

Given two equations

x + 2 y = 3  

x + 2 y - 3 = 0  .... ( i )

( k - 1 ) x + ( k + 1 ) y = ( k + 2 )

( k - 1 ) x + ( k + 1 ) y - ( k + 2 ) = 0  .....( ii )

They have no solution.

We have to find value of k

For no solution we know that

$\large \dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2} \\\\\\\large \text{putting values here}\\\\\\\large \dfrac{1}{k-1}\neq \dfrac{2}{k+1} \\\\\\\large k+1\neq 2k-2\\\\\\\large 3\neq k$

Thus we get many value of k ( 2 , 4 ....) leaving 3 .