How to Determine if an Ordered Pair Is a Solution

Introduction

In mathematics, an ordered pair is a set of two elements that are written in a specific order. Ordered pairs are often used to represent points on a graph or to represent the input and output values of a function.

To determine whether an ordered pair is a solution to an equation, we need to substitute the values from the ordered pair into the equation and see if the equation is true.

Steps for Determining if an Ordered Pair Is a Solution

1. Substitute the values from the ordered pair into the equation.
2. Evaluate the equation to simplify it into a single number.
3. Check if the result of the evaluation is equal to zero.

Additional Information

• If the result of the evaluation is zero, then the ordered pair is a solution to the equation.
• If the result of the evaluation is not zero, then the ordered pair is not a solution to the equation.
• It’s important to note that the order of the elements in an ordered pair matters.

Example

Let’s consider the equation 2x + 3y = 7 and the ordered pair (1, 2).

1. Substitute the values from the ordered pair into the equation:
   2(1) + 3(2) = 7
2. Evaluate the equation:
   2 + 6 = 7
3. Check if the result is equal to zero:
   7 = 7 (which is true)

Since the result of the evaluation is zero, the ordered pair (1, 2) is a solution to the equation 2x + 3y = 7.

Conclusion

Determining whether an ordered pair is a solution to an equation is a straightforward process that involves substituting the values into the equation, evaluating the result, and checking if it is equal to zero. By following these steps, you can easily determine if an ordered pair is a solution to a given equation.

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