### About Nonlinear Systems of Inequalities:

To solve a system of inequalities, we first sketch the graph of each inequality. Once this is done, we will look for the section of the coordinate plane that satisfies all inequalities of the system. This will be the overlap of the graphs and our solution for the system.

Test Objectives

- Demonstrate the ability to solve a system of linear inequalities
- Demonstrate the ability to solve a system of nonlinear inequalities

#1:

Instructions: Sketch the graph of each system.

$$a)\hspace{.2em}x - y > 3$$ $$2x + y > 8$$

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#2:

Instructions: Sketch the graph of each system.

$$a)\hspace{.2em}x - 4y ≥ 20$$ $$y ≤ 2x - 4$$

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#3:

Instructions: Sketch the graph of each system.

$$a)\hspace{.2em}-4x - y ≥ 3$$ $$y ≤ 2x^2 - 3$$

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#4:

Instructions: Sketch the graph of each system.

$$a)\hspace{.2em}x^2 + y^2 < 25$$ $$y > x^2 - 2$$

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#5:

Instructions: Sketch the graph of each system.

$$a)\hspace{.2em}y ≥ x^2 - 2x + 1$$ $$\frac{x^2}{16}+ \frac{y^2}{25}≤ 1$$

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}$$

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#2:

Solutions:

$$a)\hspace{.2em}$$

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#3:

Solutions:

$$a)\hspace{.2em}$$

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#4:

Solutions:

$$a)\hspace{.2em}$$

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#5:

Solutions:

$$a)\hspace{.2em}$$