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Chapter 7: Problem 38

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}x+y \leq 4 \\ y \geq 2 x-4\end{array}\right.\)

Short Answer

Expert verified
The solution is the region on the graph where the areas shaded by \(x+y \leq 4\) and \(y \geq 2x-4\) overlap.

Step by step solution

01

Graph the first inequality

To graph the inequality \(x+y \leq 4\), first graph the line with the equation \(x+y=4\). Start by sketching the y-intercept (0,4). Since the formula is in standard format, we can identify the slope as -1. Now, for every 1 unit moved to the right, move 1 unit down to draw the line. After drawing the line, shade the area under the line to represent \(\leq 4\).
02

Graph the second inequality

Next, graph the inequality \(y \geq 2x-4\). Start with the y-intercept at (0,-4). As the equation is in slope-intercept form, the slope is 2. So for every 1 unit moved to the right, move 2 units up to draw the line. After the line is drawn, shade the area above the line since \(y \geq\) is the inequality.
03

Identify the solution set

The shaded region where the two inequalities overlap represents the solution set of the system of inequalities. This is the region that satisfies both inequalities simultaneously.

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Most popular questions from this chapter

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}x \geq 4 \\ y \leq 2\end{array}\right.\)

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