Question

For which value of k will the following pair of linear equations have no solution?

3x + y = 1

(2k – 1)x + (k – 1)y = 2k + 1

Answer 1

3x + y – 1 = 0

(2k – 1)x + (k – 1)y – (2k + 1) = 0

`a_1/a_2 = 3/(2k-1)`

`b_1/b_2 = 1/(k-1)`

`c_1/c_2 = (-1)/(-2k-1) = 1/(2k+1)`

For no solutions,

`a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

`3/(2k-1) = 1/(k-1) ≠ 1/(2k+1)`

`3/(2k-1) = 1/(k-1)`

3k – 3 = 2k – 1

3k - 2k = -1 + 3

k = 2

Hence, for k = 2, the given equation has no solution.