so we assume that x=x and y=y is true for both situations so
3x+2y=-2
6x-y=6
6x-y=6
add y to both sides
6x=6+y
subtract 6 from both sides
6x-6=y
subsitute (6x-6) for y in first equation
3x+2(6x-6)=-2
distribute
3x+12x-12=-2
add like terms
15x-12=-2
add 12 to both sides
15x=10
divide both sides by 15
x=2/3
subsitute
3x+2y=-2
3(2/3)+2y=-2
6/3+2y=-2
2+2y=-2
subtract 2 from both sides
2y=-4
divide both sides by 2
y=-2
x=2/3
y=-2
solution in (x,y) form
(2/3,-2)