Question

If the system of equations
3x + y = 1
(2k – 1)x + (k – 1)y = 2k + 1
is inconsistent, then k =
A. 1
B. 0
C. – 1
D. 2

Answer 1

Answer:

k=2

Step-by-step explanation:

3/2k-1 = 1/k-1

so k value is 2 by calculating

Answer 2

Given pair of system of equations  :  

3x + y = 1

(2k – 1)x + (k – 1)y = 2k + 1

Solution :  

The given pair of  linear equation can be written as :

3x + y -1 = 0………(1)

(2k – 1)x + (k – 1)y - (2k + 1) = 0…………(2)

On comparing with General form of a pair of linear equations  

a1x + b1y + c1 = 0 and   a2x + b2y + c2 = 0 , we get :  

a1 = 3, b1 = 1, c1 = - 1

a2 = (2k – 1) , b2 = k - 1 , c2 = - (2k + 1)

We have ,  

a1/a2 = 3/(2k – 1),  b1/b2 = 1/k - 1 & c1/c2 = -5/-15 = - 1/-(2k + 1)

Given: A pair of linear equations is inconsistent ,then a1/a2 = b1/b2 ≠ c1/c2

3/(2k – 1) = 1/k - 1

3 (k - 1) = 2k - 1

3k - 3 = 2k -1

3k - 2k = - 1 + 3

k = 2

Hence, the value of k  is 2.

Among the given options option (D) 2 is correct.  

HOPE THIS ANSWER WILL HELP YOU……

 

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