System #1
2x + 3y = 12 and 4x + 3y = 18
I'd use elimination on this one; we subtract equations and the 3y disappears,
2x = 6
x = 3
3y = 18-4x = 18 - 4(3) = 18 = 12 = 6
y = 2
System #2
y = 2x +1 and y =-3x -2
Here I'd use elimination; we have two things equal to y, we eliminate y by setting the right sides equal to each other,
2x + 1 = -3x - 2
5x = -3
x = -3/5
y = 2x+1 = -1/5
check y=-3x -2 = 9/5 - 10/5 = -1/5, good
System #3
x = 2y + 5 and x + 3y = 25
Here I'd use substitution. The first equation is for x in terms of y; if we substitute it into the second equation we'll just have an equation in y.
(2y + 5) +3y = 25
5y + 5 =25
5y = 20
y = 4
x = 2y+5 = 13
