There are two equations given in the question:

2x + 3y – 9 = 0 (i)

And, 6x + (k – 2)y – (3k – 2) = 0 (ii)

These given equations are in the form a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 where,

a₁ = 2, b₁ = 3 and c₁ = – 9

Also, a₂ = 6, b₂ = (k – 2) and c₂ = – (3k – 2)

Now, for the given pair of linear equations having no solution we must have:

,

k = 11,

k = 11, 3 (3k – 2) 9 (k – 2)

∴ k = 11 and 1 3 (True)

Hence, the value of k is 11