Answer
No solution.
Work Step by Step
Step 1. Find the solutions of $x+y\gt4$ as indicated by the red shaded area.
Step 2. Find the solutions of $x+y\lt-1$ as indicated by the blue shaded area.
Step 3. The solutions for the system of inequalities should be the overlap of the above solutions; however, as there is no overlap between the two shaded areas, we get no solution for the system.
