3x - 2y = 3

-6x + 4y = -6

6x - 4y = 6

Many solutions.

This system of equations has an infinite number of solutions because the line 3x - 2y = 3 is the same equation as -6x + 4y = -6.

Proof:

3x - 2y = 3 (multiply by -2)

-6x + 4y = -6

Since we only have one equation and two variables there are an infinite number of solutions.

The equations are dependent. The number of solutions is infinite.

Divide the second equation by 2 and add to the first

.. (3x -2y) +(-6x +4y)/2 = (3) +(-6)/2

.. 0 = 0 . . . there are no unique solutions