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We need to solve each system of linear equations provided in the problem, determine the number of intersection points, and if there is one point, find the coordinates. If there are infinitely many points of intersection, we will find the parametric equations.

### Part (a):
The system of equations is:
\[
3x - 2y = 4
\]
\[
6x - 4y = 9
\]

We can use substitution, elimination, or matrix methods to solve this. Let's simplify this system by multiplying the first equation to align terms.

### Part (b):
The system of equations is:
\[
2x - 4y = 1
\]
\[
4x - 8y = 2
\]

This appears to have a similar structure as part (a), so we will simplify it and check for any redundant or dependent equations.

### Part (c):
The system of equations is:
\[
x - 2y = 0
\]
\[
x - 4y = 8
\]

This system also can be solved by substitution or elimination methods. Now, let's solve each system to find the intersections.It seems like I can't do more advanced data analysis right now. Please try again later.

Feel free to ask any questions or share any further instructions, and I'll be happy to help!

In each part, solve the linear system, if possible, and use the result to determine whether the lines represented by the equations in the system have zero, one, or infinitely many points of intersection. If there is a single point of intersection, give its coordinates, and if there are infinitely many, find parametric equations for them. (a) 3x - 2y = 4, 6x - 4y = 9 (b) 2x - 4y = 1, 4x - 8y = 2 (c) x - 2y = 0, x - 4y = 8

Solve systems of linear equations to find out whether they have zero, one, or infinitely many solutions. The problems cover solving linear systems and finding points of intersection or parametric equations. Suitable for high school students.

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