Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions?
(i) x - 3y - 3 = 0; 3x - 9y - 2 = 0
(ii) 2x + y = 5; 3x + 2y = 8
(iii) 3x - 5y = 20; 6x - 10y = 40
(iv) x - 3y - 7 = 0; 3x - 3y - 15 = 0

(i) x - 3y - 3 = 0
3x - 9y - 2 = 0
Comparing these with pair of equations of the form
a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0,
a1/a2 = 1/3, b1/b2 = -3/-9 = 1/3, c1/c2 = 3/2
=> a1/a2 = b1/b2 ≠ c1/c2, the lines have no solution
(ii) 2x + y = 5
3x + 2y = 8
a1/a2 = 2/3, b1/b2 = 1/2, c1/c2 = 5/8
=> a1/a2 ≠ b1/b2, the lines have unique solution
(iii) 3x - 5y = 20
6x - 10y = 40
a1/a2 = 3/6 = 1/2, b1/b2 = -5/-10 = 1/2, c1/c2 = 20/40 = 1/2
=> a1/a2 = b1/b2 = c1/c2, the lines have infinitely many solutions
(iv) x - 3y - 7 = 0; 3x - 3y - 15 = 0
a1/a2 = 1/3, b1/b2 = -3/-3 = 1, c1/c2 = 7/15
=> a1/a2 ≠ b1/b2, the lines have unique solution.