Chapter 5: Q. 298 (page 672)

In the following exercises, solve each system by graphing.
$\{\begin{cases} y \leq \frac{- 2}{3} x + 5 \\ x \geq 3 \end{cases}$

Short Answer

Expert verified

The solution set is the region shaded with the darker color including the boundary lines.

Step by step solution

Step 1. Given Information

The given system is $\{\begin{cases} y \leq \frac{- 2}{3} x + 5 \\ x \geq 3 \end{cases}$

Step 2. Plot the first inequality

The intercepts of $y = \frac{- 2}{3} x + 5$ are $(0, 5), (7.5, 0)$ .
Join the points to plot a solid line.
The point $(0, 0)$ satisfies the inequality, so shade the region that includes the origin.

Step 3. Plot the second inequality

The line $x = 3$ will be a vertical line passing through $(3, 0)$ .
Draw a vertical line that is solid on the same graph.
The point (0,0) does not satisfy the inequality, so shade the region that excludes the origin.

The solution set is the region shaded with the darker color including the boundary lines.

Step 4. Check the Solution

One of the points that lie in the solution set is $(4, 0)$ .
Check if the point satisfies the inequalities.

$0 \overset{?}{\leq} 0 + 5 0 \leq 5$

$0 \geq 3$

As both the inequalities are satisfied, the solution is verified.

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In the following exercises, solve each system by graphing.
$\{\begin{cases} y \leq \frac{- 2}{3} x + 5 \\ x \geq 3 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Plot the first inequality

Step 3. Plot the second inequality

Step 4. Check the Solution

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In the following exercises, solve each system by graphing.y≤-23x+5x≥3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Plot the first inequality

Step 3. Plot the second inequality

Step 4. Check the Solution

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, solve each system by graphing.
$\{\begin{cases} y \leq \frac{- 2}{3} x + 5 \\ x \geq 3 \end{cases}$