Нелінійні нерівності: як виглядає графік, якщо розв'язків немає?

A graph of nonlinear inequalities that has no solutions has no overlapping sections.

Here's the graph of the system: $\\\begin{cases}x^2+2x-1<y\\-x^2+3x+-2>y\end{cases}$

Notice that the graphs don't overlap at any point. That means there's no set of points that satisfies both equations so we say there's no solution.

Systems of Nonlinear Inequalities with No Solutions

In the previous lessons, you were able to learn how to graph systems of nonlinear inequalities. The method is very similar to learning to graph systems of linear inequalities. You may also recall how to graph linear systems.

Check out this lesson on graphing a linear inequality.

Above, I have graphed the following system:

$$\begin{align} y>x^{2}-2 \\ y<(x+2)^{2}-2 \\ \end{align}$$

The boundary lines are the normal graph for inequalities.

Looking Further

Other nonlinear systems include a parabola and a line. Next lessons will discuss using the quadratic formula and using elimination.

(Video) Systems of Nonlinear Inequalities with No Solution

by Anusha Rahman

In this video by Anusha Rahman, you will learn how to solve a system of nonlinear inequalities with no solution.