Question

6. If the system of equations 3x + y = 1 and, (2x - 1) x + (k - 1) y = 2k + 1 is inconsistent, then k = (a) 1 (b) 0 (c)-1 (d) 2​

Answer 1

Step-by-step explanation:

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 = 2Read 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