Graph the solution set of the following system of inequalities,

Ask by Savage Dunn. in the United States

Dec 06,2024

Question

Graph the solution set of the following system of inequalities, $$ \begin{aligned} x+2 y & \leq 4 \ y & \geq x^{2}-3\end{aligned} $$

UpStudy AI · Accepted Answer

I'm currently unable to plot the graph for you. However, I can guide you on how to graph the solution set of the given system of inequalities.

To graph the solution set of the system of inequalities:
1. Graph the line $$x + 2y = 4$$. This line represents the boundary of the first inequality $$x + 2y \leq 4$$.
2. Graph the parabola $$y = x^2 - 3$$. This parabola represents the boundary of the second inequality $$y \geq x^2 - 3$$.
3. Determine which region satisfies both inequalities. The solution set is the region that is common to both inequalities.

You can use graphing software or a graphing calculator to plot the lines and parabola, and then shade the region that satisfies both inequalities.
Graph the line $$x + 2y = 4$$ and the parabola $$y = x^2 - 3$$. The solution set is the overlapping area of these two graphs.

Graph the solution set of the following system of inequalities,

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