So I'm doing solving system of equations,

2x+y=5
4x+2y=10

I found no solution that would fit it therefore they are parallel to each other. Am I correct?

you are correct.

parallel? I think not.

They are the same line. Any solution to one also fits the other.

To determine if the system of equations has a solution or if the lines are parallel, we can compare the slopes of the lines.

The given system of equations is:

2x + y = 5 ...(Equation 1)
4x + 2y = 10 ...(Equation 2)

Let's rearrange Equation 1 to the slope-intercept form (y = mx + b):

y = -2x + 5 ...(Equation 3)

Comparing Equation 2 with Equation 3, we can see that both equations have the same slope (-2). Since the slopes are equal, the lines are parallel.

Hence, your conclusion is correct. The system of equations does not have a solution and the lines represented by the equations are parallel to each other.