Example

Use the graph to determine which ordered pairs plotted below are solutions of the inequality [latex]x–y<3[/latex].

Answer: Solutions will be located in the shaded region. Since this is a “less than” problem, ordered pairs on the boundary line are not included in the solution set. These values are located in the shaded region, so are solutions. (When substituted into the inequality [latex]x–y<3[/latex], they produce true statements.)

[latex](−1,1)[/latex]

[latex](−2,−2)[/latex]

These values are not located in the shaded region, so are not solutions. (When substituted into the inequality [latex]x-y<3[/latex], they produce false statements.)

[latex](1,−2)[/latex]

[latex](3,−2)[/latex]

[latex](4,0)[/latex]

Answer

[latex](−1,1)\,\,\,(−2,−2)[/latex]

Example

Is [latex](2,−3)[/latex] a solution of the inequality [latex]y<−3x+1[/latex]?

Answer: If [latex](2,−3)[/latex] is a solution, then it will yield a true statement when substituted into the inequality [latex]y<−3x+1[/latex].

[latex]y<−3x+1[/latex]

Substitute [latex]x=2[/latex] and [latex]y=−3[/latex] into inequality.

[latex]−3<−3\left(2\right)+1[/latex]

Evaluate.

[latex]\begin{array}{l}−3<−6+1\\−3<−5\end{array}[/latex]

This statement is not true, so the ordered pair [latex](2,−3)[/latex] is not a solution.

Answer

[latex](2,−3)[/latex] is not a solution.