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To find the number of solutions, we can solve the system of equations.
Let's start by rearranging the equations to solve for y:
2x + y = 3 --> y = 3 - 2x
6x = 9 - 3y --> 3y = 9 - 6x --> y = 3 - 2x
Since both equations are equivalent, it means they represent the same line. Therefore, the system has infinitely many solutions.
Therefore, the answer is C. infinite.