Exercise 3 Page 286

If we examine the system of inequalities we notice that one has a boundary line with a positive slope and the other one has a negative slope. Knowing this, we can match the positively sloped inequality with the upward slanting boundary line and vice-versa. We also label a point that is inside the shaded area. It will come in handy! To check which inequality symbol we should replace the equal sign with, we can use the test point $(2,6)$ and substitute it into each of the inequalities. Since it is inside the shaded area each inequality should form a true statement for this point. As $6$ is greater than $4,$ for this to form a true statement we have to use either $>$ or $\ge .$ However, since the boundary line is solid, we should use $\ge .$ Let's also test the point in the second inequality. For this to form a true statement,we have to use either $>$ or $\ge .$ However, since the boundary lines is dashed, we should use $>.$ Finally, we have the following system of inequalities.