Example: Does the point (5, 2) lie within the solution set of the given system of inequalities?
y ≤ x − 5
y ≥ −x − 4
Focus on the first inequality. Does (5,2) satisfy this inequality? Is 2 ≤ 5 - 0 true? Yes, it is true. Before we call (5,2) a solution, we must determine whether or not (5,2) also satisfies the 2nd inequality: Is 2 ≥ -(5) - 4 true?
Is 2 ≥ -9? Yes! So, yes, (5,2) is a solution of this system of inequalities.
We must check out the other three possible solutions in the same fashion.
Try out the point (5,-2). Does it satisfy both inequalities?
Focusing on the first inequality: Is -2 ≤ 5 - 5 true? Yes, it is. The key question here and now is whether or not (5,-2) also satisfies y ≥ −x − 4. Is
-2 ≥ -(5) - 4 true? Is -2 ≥ -9 true? Yes. Thus, (5,-2) satisfies both inequalities and is thus another solution.
Check out (-5,2) and (-5,-2) in precisely the same way. Is either one, or are both, a solution (or solutions) to the given set of inequalities?
