Solve each of the following systems, if possible. Indicate whether the system has a unique solution, infinitely many solutions or no solution.

x- 2y=3
4y- 2x=0

To solve the given system of equations:

Step 1: We can start by rewriting the equations in standard form, which is when the coefficients of x and y are positive integers.

Given system:
x - 2y = 3 -- Equation 1
-2x + 4y = 0 -- Equation 2

Step 2: Let's multiply both sides of Equation 1 by 2 to get rid of the fraction:
2(x - 2y) = 2(3)
2x - 4y = 6 -- Equation 3

Step 3: Now we can subtract Equation 2 from Equation 3 to eliminate x:
(2x - 4y) - (-2x + 4y) = 6 - 0
2x - 4y + 2x - 4y = 6
4x - 8y = 6 -- Equation 4

Step 4: Equation 4 is equivalent to 2 times Equation 1. This tells us that Equation 4 is not an independent equation. Therefore, it does not change the information from the given system.

Step 5: Now, let's compare the original Equation 1 and Equation 3:
Equation 1: x - 2y = 3
Equation 3: 2x - 4y = 6

As we can see, Equation 3 is the result of multiplying Equation 1 by 2. Both equations represent the same line in the xy-plane. Therefore, they are dependent equations and have infinitely many solutions.

To summarize, the system of equations has infinitely many solutions.