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Chapter 7: Problem 29

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}x \geq 2 \\ y \leq 3\end{array}\right.\)

Short Answer

Expert verified
The solution set of the given system of inequalities includes all points in the plane that are right of or on the line \(x = 2\) and below or on the line \(y = 3\).

Step by step solution

01

Understand the System of Inequalities

We have two inequalities here. The inequality \(x \geq 2\) indicates all values of x that are greater than or equal to 2. The inequality \(y \leq 3\) indicates all values of y that are less than or equal to 3.
02

Graph the Inequalities

We will graph these inequalities on a coordinate plane. Start with the inequality \(x \geq 2\). On a graph, this is a vertical line passing through the point (2,0) and all the x-values to the right of this line, including the line, are part of the solution. Then graph \(y \leq 3\). On a graph, this is a horizontal line passing through the point (0,3) and all the y-values below this line, including the line, are part of its solution.
03

Find the Solution to the System of Inequalities

The solution to the system of inequalities is the region where the inequalities intersect. In this case, that will be all the points right of or on the line \(x = 2\) and below or on the line \(y= 3\).

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Most popular questions from this chapter

The graphs of solution sets of systems of inequalities involve finding the intersection of the solution sets of two or more inequalities. By contrast, in Exercises 43-44, you will be graphing the union of the solution sets of two inequalities. Graph the union of \(x-y \geq-1\) and \(5 x-2 y \leq 10\).

Graph each linear inequality. \(5 x+3 y \leq-15\)

a. Determine if the parabola whose equation is given opens upward or downward. b. Find the vertex. c. Find the \(x\)-intercepts. d. Find the \(y\)-intercept. e. Use (a)-(d) to graph the quadratic function. \(f(x)=x^{2}-2 x-8\)

Graph each linear inequality. \(y>\frac{1}{3} x\)

Graph each linear inequality. \(y \geq 0\)
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