Graph each function in the system of inequalities as an equation. Use a dotted line to denote nonlinear functions, and use a solid line to denote linear ones. To graph a function, draw a two-column table with columns for x-values and y-values. Select a value for either x or y and plug it into the equation. Solve for the other variable.
Shade lightly one side of each inequality according to the sign of the inequality. For example, the inequality x^2 +y^2 < 25 means that the solution to the inequality is every point inside a circle with radius 5, but not the circle itself. The solution to the inequality y > x^2 is everything outside the parabola drawn by y=x^2.
Find the shaded area where the solution sets of each inequality meet. Shade this area darker. This is your solution to the nonlinear system of inequalities. You can erase the shaded areas that are not part of the solution if you used a pencil.