Well to solve by graphing, you would graph both equations and then see where the two lines intersect. This graphical intersection is the point where both equations are equal to each other.
To solve using math :P
If a solution exists, (x,y)=(x,y) so we can say y=y and then we can say:
2x+3=-x add x to both sides
3x+3=0
3(x+1)=0
So x=-1, and since y=-x
y=1
So the solution to the system of equations, and the graphical intersection, is the point (-1, 1)