Exercise 39 Page 332

To solve the given system by graphing, we should first draw each inequality separately. Then we will combine the graphs. The overlapping region will be the solution set. Let's start!

Inequality I

To determine the boundary line of the first inequality, we need to exchange the inequality symbol for an equals sign. This boundary line is a horizontal line. The inequality $y\le 5$ describes all values of $y$ that are less than or equal to $5.$ This means that every coordinate pair with an $y\text{-value}$ that is less than or equal to $5$ needs to be included in the shaded region. Notice that the inequality is non-strict, so the boundary line will be solid.

Inequality II

Now that we have completed the first inequality, let's determine the boundary line of the second inequality. We will follow the same process once more.