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