Remember that the points that are solutions to the system of linear inequalities satisfy both inequalities. What information does the inequality symbols provide?
See solution.
Practice makes perfect
There are two ways to tell if a point is part of the solution set of a system of linear inequalities. One is by substituting it in the inequalities directly to test it. Besides that, such as in the case that the point lies one the boundary lines, we can know if it belongs to the solution set by looking at the inequality symbols.
Substituting the point
Recall that the points that are solutions to the system are those which satisfy both inequalities. To know if (-4, 6) is a solution of the system all we need to do is substitute it into the inequalities. Let's see an example.
Example system
y≥ x+7 & (I) y ≥ - x -1 & (II)
Let's substitute the point in Inequality (I) to test it.
Once again the inequality holds true. Therefore, the point is part of the solution set for Inequality (II) and it is part of the solution set for the system.
Point lying on the boundary lines
The inequality symbol we use gives us information about the solution set. The symbols ≤ and ≥ tell us that the boundary line is included in the solution set. Therefore, if the point lies on the boundary line in these cases, we can already tell that it is part of the solution set for the inequality.
Notice that it must be on both boundary lines for it to be part of the system's solution.
On the other hand, the symbols < and > tell us that the boundary line is not included in the solution set. In these cases, even if the point lies in both boundary lines at the same time, it will not be part of the system's solution set.
