The system of second-degree quadratic inequalities involves multiple inequalities with a common variable. Each inequality is in the form a_i x^2 + b_i x + c_i R_i 0, where a_i ≠ 0 and R_i ∈ {>, <, ≥, ≤}. The solution of the system is the intersection of the solution sets of each inequality. Methods of analyzing discriminants, roots, and signs are used in solving inequalities