How do you solve this simultaneous equation?

Relative values of x:
2x + 5y = 12
2x = 12 - 5y
x = (12 - 5y)/2

x - 6y = - 11
x = 6y - 11

Value of y:
12 - 5y = 2(6y - 11)
12 - 5y = 12y - 22
17y = 34
y = 2

Value of x (1st equation):
= (12 - 5[2])/2
= (12 - 10)/2
= 2/2 or 1

Answer: x = 1, y = 2

Proof (2nd equation):
1 - 6(2) = - 11
1 - 12 = - 11
- 11 = - 11

2x + 5y = 12 (solve by using substitution)
x - 6y = -11

x - 6y = -11
x = 6y - 11

2x + 5y = 12
2(6y - 11) + 5y = 12
12y - 22 + 5y = 12
12y + 5y = 12 + 22
17y = 34
y = 34/17
y = 2

x - 6y = -11
x - 6(2) = -11
x - 12 = -11
x = 12 - 11
x = 1

∴ x = 1 , y = 2

12x + 30 y = 72
5x - 30y = - 55-------ADD

17x = 17
x = 1

2 + 5y = 12
y = 2

x = 1 , y = 2