I am trying to solve the simultaneous equations by algebraic method, I know the solutions for "a" and "b" are 0.46 and -5.2, I have used a few different methods and the latest is close but not correct.

Using elimination method I came up with;

12a + 3b = - 10

3a - 9b = 17

36a + 9b = - 30

9a - 9b = 51

36 - ( - 9)a + (9 - 9)b = -30 + 51

41a = 21

a = 0.512

3a - 3b = 17

3(0.512) - 3b = 17

6.15 - 3b = 17

3b = 17 - 6.15

b = -5.38

12(0.512) + 3(-5.38) = -10

3(0.512) - (-16.14) = 17.69

As can be seen by the solutions they are not a million miles out, but somewhere I am making an error?