The Monterey Institute explains that the graph of a linear inequality has a shaded region and that a set of ordered points (x, y) may be located within or outside of the shaded region. To find the values of x and y that satisfy an inequality, one must obtain a pair of ordered points within the region that satisfies the inequality, which includes the continuous boundary line.
Ordered pairs that have values that, when substituted into the linear inequality, make the inequality a true statement are the same pairs that satisfy the inequality. The opposite is true for ordered pairs with values that make the inequality a false statement.
A crucial point to note in finding the correct values of x and y is that if the graph plotted has a continuous boundary line, it means that ordered pairs of points located on the line are part of the solution. However, ordered pairs located on broken boundary lines are not part of the solution and must not be considered as viable points. In such a case, consider only the ordered pairs that lie within the appropriate region. An easy way to find ordered pairs that satisfy the inequality is to create a table of values.