Question

3x-6y=9
x=2y+3
how many solutions are there

Answer 1

Infinitely many. Substituting x = 2y + 3 into 3x − 6y = 9 gives 3(2y+3) − 6y = 9 → 9 = 9, an identity. So every y works, with x = 2y + 3. Parametrically: (x,y) = (2t+3, t) for any real t.