Part 1 : when solving systems of equations, how do you determine what method to use?

part 2 : choose 1 system of equations from the choices below. then, solve the system and post your solution, showing your steps so that other students can see which method you chose.

–y + 3x = 6
y = –6x + 12

6x – 4y = 54
–9x + 2y = –69

2y = x + 1
–2x – y = 7

Part 1. The selection of method to use for solving system of equations is a matter of arbitrary choice. That is, what's convenient for you. For me, elimination is easier.
Part 2. I'll try solving the second system.6x-4y = 54-9x+2y = -69
Multiplying the first equation by 9 and the second equation by 6.
 54x - 36y = 486-54x + 12y = -414
Adding the two equations,
-24y = 72y = -3
Subtitute back to one of the equations,-9x + 2y = -69-9x + 2(-3) = -6969 - 6 = 9x9x = 63x = 7
The solution is then (7, -3).