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Solutions to Linear Inequalities

A SOLUTION to a linear inequality of 2 variables is an ordered pair (x, y) whose coordinates satisfy the original inequality (i.e. make the original inequality true.) For example, note the point (5, 3) shown in the applet below. The graph of the inequality is also shown. (5, 3) is a SOLUTION to the inequality because ==> which is TRUE! Any point (x, y) that does NOT satisfy the original inequality (that is, does NOT make the original inequality true) is said NOT to be a solution to the given inequality. How many solutions (x, y) does the graph of an linear inequality of two variables have?


Change the parameters A, B, and C by using the sliders or by inputting values in the input boxes. Drag the yellow point around in the graph of this linear inequality. Algebraically show that this point is a SOLUTION to this linear inequality.


Pick a point (x, y) that does NOT lie in the graph of the shaded blue region. Show that this point is NOT a solution to this linear inequality.