Beyonce is solving a system of equations: 2x – 3y = -2 4x + y = 24
She multiplies the second equation by 3 and adds it to the first equation to find 14x = 70, showing her that x = 5. Beyonce finds that y = 4.
Step 1: 3(4x + y = 24) → 12x + 3y = 72
Step 2: 2x – 3y = -2
+ 12x + 3y = 72
14x = 70
14x/14= 70/14 → x = 5

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.
Step 1: -2(2x – 3y = -2) → -4x + 6y = 4
Step 2: -4x + 6y = 4
+ 4x + y = 24
7y= 28
7y/7= 28/7 → y = 4

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?
If Beyonce uses a different method, would she get the same solution? Be sure to show work or explain your reasoning.

If there is no solution or an infinite number of solutions to the system of equations, would it matter which method you used to solve the system? Be sure to explain your reasoning/