Question

5. If the system of equations 4x + 3y = 7 and
(k - 1)x + (2k - 1)y = 3k + 1 is inconsistent, then
find the value of k.​

Answer 1

The value of k is 3/2.

Step-by-step explanation:

Given that,

4x + y = 3

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

A.T.Q.

The Equation is inconsistent, then

$a_{1}/a_{2}= b_{1}/b_{2}≠ c_{1} /c_{2}$

so, as per the equation,

$a_{1}= 4, b_{1} = 1, c_{1}= -3$

$a_{2}= 2k-1, b_{2}= (k-1), c_{2} = -(2k+1)$

so,

a1/a2 = b1/b2

4/(2k-1) = 1/(k-1)

4k-4 = 2k-1

4k-2k = -1 + 4

2k = 3

k = 3/2

Thus, k = 3/2