May I please have some help on this? I will give and 25pts

Beyonce finds that y=4. Thinking about this process, Beyonce says out loud, “There are lots of ways I could go about solving this problem. I could do the method above or I could multiply the first equation by -2 and add the second. I seem to find that there is only one solution to the two equations but I wonder if I will get the same solution if I use a different method?

2. Is the answer to 1 (can you get the same solution even if you use different methods) different if we have a system of two equations with no solutions? What if there are infinite solutions? Or is it the same process? Beyonce is solving a system of equations: 2x-3y=-2 and 4x+y=24 She multiplies the second equation by 3 and then adds the first equation to find 14x=-70, showing her that x=5.

Here is my answer to the first one can you help me with the second?
1. What is the answer to Beyonce's question? Be sure to show work or explain reasoning.
x=5, y=4. (5, 4)

My Work:
2x-3y=-2 [1]
4x+y=2 [2]
Multiply [1] by -2 and add to [2] gives -4x+6y=4 [3]
Add [2] and [3] term by term
(4x-4x) ++ (y+6y) = (24+4), that is 7y=28 (divide by both sides of the equation)
y=4
Substitute y=4 into either 2 equations
Substituting y=4 into [2]
4x+4=24 (Make sure to subtract 4 from both sides)
4x=20(Divide both sides by 4)
x=5