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Chapter 7: Problem 31

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}x \leq 5 \\ y>-3\end{array}\right.\)

Short Answer

Expert verified
The solution set of the system of inequalities \(x \leq 5\) and \(y > -3\) is the region of the coordinate plane that is to the left of the solid line \(x=5\) and above the dashed line \(y=-3\).

Step by step solution

01

Express Inequalities in Line Format

The given inequalities\(x \leq 5\) and \(y > -3\) are already in the format that can be represented graphically. Therefore, For the first inequality: \(x = 5\) is a vertical line passing through \(x = 5\),And for the second inequality: \(y = -3\) is a horizontal line passing through \(y = -3\).
02

Graph the Inequalities

To graph the first inequality \(x \leq 5\), draw a solid vertical line through \(x = 5\) since it is \(x \leq 5\) (equal to is included hence solid line). Shade to the left of the line because \(x\) is less than or equals to 5.For the second inequality \(y > -3\), draw a dashed horizontal line through \(y = -3\) because it is \(y > -3\) (not equals to, hence dashed line). Shade above the line because \(y\) is greater than -3.
03

Identify the Solution Set

The solution set for the system of inequalities lies in the region where the shadings for both inequalities overlap. This falls in the area that is to the left of the solid line \(x=5\) and above the dashed line \(y=-3\).

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Most popular questions from this chapter

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