Combined Nonlinear Systems of Equations and Inequalities

Consider the following equation-inequality system:

$$x^2 + y = 0$$ $$(x + y)^2 + 4e^{\frac{x}{2} + \frac{y}{2}} \leq 2(x^2 + e^x + y^2 + e^y)$$

Which of the following is the set of solutions for this system?