![]() ![]() Let’s take a look at one more example: the inequality 3 x + 2 y ≤ 6. However, had the inequality been x ≥ y (read as “ x is greater than or equal to y"), then (−2, −2) would have been included (and the line would have been represented by a solid line, not a dashed line). It is not a solution as −2 is not greater than −2. The ordered pair (−2, −2) is on the boundary line. In these ordered pairs, the x-coordinate is smaller than the y-coordinate, so they are not included in the set of solutions for the inequality. The ordered pairs (−3, 3) and (2, 3) are outside of the shaded area. These ordered pairs are in the solution set of the equation x > y. In these ordered pairs, the x-coordinate is larger than the y-coordinate. The ordered pairs (4, 0) and (0, −3) lie inside the shaded region. Is the x-coordinate greater than the y-coordinate? Does the ordered pair sit inside or outside of the shaded region? The graph below shows the region x > y as well as some ordered pairs on the coordinate plane. Let’s think about it for a moment-if x > y, then a graph of x > y will show all ordered pairs ( x, y) for which the x-coordinate is greater than the y-coordinate. Remember how all points on a line are solutions to the linear equation of the line? Well, all points in a region are solutions to the linear inequality representing that region. This region (excluding the line x = y) represents the entire set of solutions for the inequality x > y. ![]() Next, look at the light red region that is to the right of the line. First, look at the dashed red boundary line: this is the graph of the related linear equation x = y. The solution is a region, which is shaded. ![]() Here is what the inequality x > y looks like. One way to visualize two-variable inequalities is to plot them on a coordinate plane. Equations use the symbol = inequalities will be represented by the symbols, and ≥. Inequalities and equations are both math statements that compare two values.
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