Exercise 33 Page 261

Notice that Sides (I) and (III) are vertical lines while Sides (II) and (IV) are horizontal. It follows then that the boundary line for the corresponding inequalities will take the following form. Side (I) & (III):& x=... Side (II) & (IV):& y=... In each equation the variable will be equal to the value on the axis that the line passes through. For example, notice that Side (I) intersects the x-axis at x=- 1. Therefore, the equation for that boundary line is x=- 1. Let's examine the other lines. Side (I):& x=- 1 Side (II):& y=- 3 Side (III):& x=6 Side (IV):& y=1 To determine the actual inequalities all we need to do is to replace the equal signs in the above equations with the correct inequality symbol. Since the sides of the rectangle are solid, we have two options. ≤ or ≥ We can use any point from inside the rectangle to determine which symbol is correct. Notice that (0,0) is a point inside the rectangle. This means when we substitute that point into any of the equations a true statement is made.

Replacing 0 with the correct variable for each of the inequalities, we get the following system of inequality. x ≥ - 1 & (I) y ≥ - 3 & (II) x ≤ 6 & (III) y ≤ 1 & (IV)