Problem 88 - College Algebra Essentials

Question

How do you determine if an ordered pair is a solution of an inequality in two variables, \(x\) and \(y ?\)

Step-by-Step Solution

Answer

To check if an ordered pair is a solution to an inequality in two variables \(x\) and \(y\), one should substitute the values of the ordered pair in place of \(x\) and \(y\) in the inequality, and then verify if the inequality holds true. If it does, the ordered pair is a solution. If it doesn't, it is not a solution.

Step 1: Understand the Inequality

Begin with understanding the given inequality with two variables, \(x\) and \(y\). Ensure that the inequality is in a suitable form for easy substitution, for instance, standard form or slope-intercept form.

Step 2: Obtain the Ordered Pair

Identify the ordered pair you need to verify. Ordered pairs are given in the format (x,y), where the first value represents the value of \(x\) and the second value is the value of \(y\).

Step 3: Substitution

Substitute the ordered pair's values into the inequality for corresponding variable. Replace \(x\) with the first value of the ordered pair and \(y\) with the second value.

Step 4: Verify the Inequality

After substituting the values, solve any arithmetic that is required and then verify if the inequality is true or not. If the inequality holds, then the ordered pair is an solution to the inequality. If it does not hold, then the ordered pair is not a solution of the inequality.