Q. 64.3( 6 Votes )

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 :

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:



3 (k – 1) = 2k – 1 3k – 3 = 2k – 1 k = 3 – 1 k = 2


Therefore = =


Putting the value of k we calculate


After comparing the ratio we find


So the given system of equations are inconsistent.


The value of k for which the system of equations is inconsistent is k = 2

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