How do we determine whether or not an ordered pair is a solution to a given inequality?

Suppose the inequality is 4x + 3y > 19 and the ordered pair is (2, 6)

Substitute 2 for x and 6 for y in the inequality.

4(2) + 3(6) > 19

8 + 18 > 19

26 > 19.

Since that is true, the ordered pair is a solution. If the statement was false, the ordered pair is not a solution.

If you have a graph of an inequality and want to know what portion of the graph is part of the solution, pick an ordered pair on either side of the line and substitute the value into the equation as done above. If the statement is true, that side of the line is shaded to represent the solution region. If if the statement is false, the other side of the line is shaded to represent the solution region.

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