we have the system
3x +y = -3
3x +y = 3
In this problem we have two different parallel lines
Remember that the solution of the system is the intersection point both lines
In this problem the lines don't intersect (are parallel)
therefore
the system has no solution NS
isolate the variable y in the first equation
y=-3x-3 -----> equation 1
isolate the variable y in the second equation
y=-3x+3 -----> equation 2
Solve the system of equations
equate equation 1 and equation 2
-3x-3=-3x+3
solve for x
-3x+3x=3+3
0=6 ------> is not true
that means
the system has no solution (NS)