3x+3y=6 and 5x-6y=15

Multiply first equaton by 2 and add to the other equation

6x+6y=12

5x-6y=15 +

11x+0y=27

11x=27

divide both sides by 11

x=27/11

sub back

3x+3y=6

divide both sides by 3

x+y=2

(27/11) + y=2

2 and 5/11+y=2

minus 2 and 5/11 both sides

y=-5/11

x=27/11

y=-5/11

(27/11,-5/11)