# If the system of equations3x + y = 1(2k – 1)x + (k – 1)y = 2k + 1is inconsistent, then k =A. 1B. 0C. – 1D. 2

Given:

Equation 1: 3x + y = 1

Equation 2: (2k – 1)x + (k – 1)y = (2k + 1)

Both the equations are in the form of :

a1x + b1y = c1 & a2x + b2y = c2 where

a1 & a2 are the coefficients of x

b1 & b2 are the coefficients of y

c1 & c2 are the constants

For the system of linear equations to have no solutions we must have ………(i)

According to the problem:

a1 = 3

a2 = (2k – 1)

b1 = 1

b2 = (k – 1)

c1 = 1

c2 = (2k + 1)

Putting the above values in equation (i) and solving we get:

### Thevalue of k for which the system of equations is inconsistent is k = 2

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