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In mathematics, an ordered pair is a pair of elements written in a specific order. It is typically denoted as \((x, y)\), where \(x\) and \(y\) are elements that can represent coordinates on a graph or values in a mathematical expression. In the context of inequalities, ordered pairs are used to test whether their substitution into an inequality results in a true or false statement.

Ordered pairs are fundamental in defining relations and functions. They allow us to determine solutions by substituting different values into expressions or inequalities. This helps to check the validity and solutions of various mathematical problems. In our exercise, the ordered pairs \( (0,0) \) and \( (-6,3) \) were used to test the inequality \(x+y>-3\). By substituting the pair's values into the equation, we can determine if they satisfy the inequality and thus qualify as its solutions.

Solution verification is the process of determining whether a particular input, such as an ordered pair, satisfies the conditions of a mathematical statement, like an equation or an inequality. This involves substituting the values into the given condition and checking if the resulting statement is true.

In our exercise, solution verification was done by replacing \(x\) and \(y\) with the coordinates of the ordered pairs in the inequality \(x+y>-3\). For the ordered pair \( (0,0) \), substituting gives us \(0 + 0 > -3\), which simplifies to \(0 > -3\), a true statement. Therefore, \( (0,0) \) is a solution.

• First substitute the values
• Simplify the expression
• Determine if the inequality holds

By following these steps, you can verify if any ordered pair is a solution to an inequality.

The substitution method is a technique used in mathematics to solve equations or inequalities by replacing one or more variables with specific values or other expressions. This method helps to simplify the problem, allowing us to easily determine whether given inputs satisfy the original equation or inequality.

In this exercise, the substitution method involves the following steps:

• Identify the ordered pair to be tested
• Replace \(x\) and \(y\) in the inequality \(x+y>-3\) with the values from the ordered pairs
• Simplify the expressions to find out whether they are true or false.

For the pair \( (-6,3) \), substitution in the inequality yields \(-6 + 3 > -3\), which simplifies to \(-3 > -3\). This is false because \(-3\) is not greater than \(-3\). Thus, \( (-6,3) \) does not solve the inequality.

Using the substitution method ensures clarity and precision when determining solutions for inequalities or any other equations.