Chapter 10, Problem 19RCC

To determine

To solve: graph the solution set of a system of inequalities.

Answer to Problem 19RCC

This region in completely to distinguish it from the other shaded regions.

Explanation of Solution

Given:

Calculation:

In order to graph the solution set of a system of inequalities, must first graph each individual inequality:

Given an inequality in two variables x and y, we first graph the shape of the equation $y=f\left(x\right)$ . Where $f\left(x\right)$ is some function of X, using either a dashed or solid line.

Use a dashed line if the inequality is a strict inequality of the form $y<f\left(x\right)$ or $y>f\left(x\right)$ to show that Y is never equal to the values $f\left(x\right)$ .

Otherwise, graph the equation using a solid line as usual. After graphing the shape of the curve $y=f\left(x\right)$ , must shade in the region above or below the curve.

Shade below the curve if the inequality is of the form $y<f\left(x\right)$ or $y\le f\left(x\right)$

Otherwise, shade above the curve for the inequalities of the form $y>f\left(x\right)$ or $y\ge f\left(x\right)$

After each inequality in the system has been graphed.

Look at the intersections of the regions shaded in for each equation.

The region in which all of the inequalities intersect corresponds to the solution set of the system. It is bounded by each of the equations in the system, plotted using solid or dashed lines that indicate whether the points on those points are part of the solution set.

Shade this region in completely to distinguish it from the other shaded regions.

Conclusion:

Therefore, This region in completely to distinguish it from the other shaded regions.