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
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