Chapter 8.9, Problem 15E

To determine

To find:

An ordered pair that is a solution of $y\le x+5$ , but is not a solution of $y<x+5$ .

Answer to Problem 15E

The ordered pair (0,5) is a solution of $y\le x+5$ , but is not a solution of $y<x+5$ .

Explanation of Solution

Given:

You have a gift certificate for $40 to use at a movie theater. Matinees cost $5 and evening shows cost $8.

Calculation:

Upon looking at inequality $y\le x+5$ , we can see that the points on boundary line will be solution of this equality as we have a less than or equal to sign $(\le )$ . While the points on boundary line of inequality are not solutions for $y<x+5$ as we have a less than sign $(<)$ .

We can see that both inequalities are in slope-intercept form and passes through the point (0,5).

Since point sits on boundary line of both inequalities, so it will be solution for only $y\le x+5$ .

Therefore, ordered pair (0,5) is a solution of $y\le x+5$ , but is not a solution of $y<x+5$ .