Working out simultaneous equations
3x - 4y = 11
5x + 6y =12

Firstly, label the eqns.

3x - 4y = 11 — (1)
5x + 6y = 12 — (2)

lets say that we want to eliminate x from the equation.

from (1):
3x-4y=11
15x-20y=55 — (3)

from (2):
5x+6y=12
15x+18y=36 — (4)

( make 15x the common variable )
so, ( 3 ) - ( 4 ) :
( 15x -20y ) - ( 15x+18y ) = 55 - 36
15x - 20y - 15x + 18y = 19
-2y = 19
-y = 9.5
y = -9.5
now that we know the value of y,
sub y = -9.5 into (1)
3x - 4(-9.5) = 11
3x + 38 = 11
3x = 11 - 38
x = -9

thus, x = -9, y = -9.5