Final answer:
To find the solution to a nonlinear system of inequalities, you can use a graphical method or an algebraic method. One way to solve it graphically is to plot the inequalities on a coordinate plane and find the shaded region where they overlap. Another method is to algebraically solve the system by using substitution or elimination.
Step-by-step explanation:
To find the solution to a nonlinear system of inequalities, you can use a graphical method or an algebraic method. One way to solve it graphically is to plot the inequalities on a coordinate plane and find the shaded region where they overlap. Another method is to algebraically solve the system by using substitution or elimination.
For example, let's consider the system:
5x + y < 10
2x - y > 4
We can solve this system algebraically by elimination. Multiply the first inequality by 2 and the second inequality by 5 to eliminate y:
10x + 2y < 20
10x - 5y > 20
Now, add the two equations:
20x - 3y < 40
This is the new inequality after the elimination step. To find the solution, graph the original inequalities on a coordinate plane and shade the region where they overlap, or continue solving algebraically if possible.