91Ó°ÊÓ

An ordered pair is simply a set of two numbers written in a specific order within parentheses, like (x, y). This representation is often used to show points on a graph or to illustrate solutions of equations. In the context of solving linear equations, ordered pairs indicate potential solutions.

• The first number in the pair is the x-coordinate, representing the horizontal position on a graph.
• The second number is the y-coordinate, denoting the vertical position.

To determine if an ordered pair is a solution of an equation, substitute the x and y values from the pair into the equation. If the equation is true after the substitution, then the ordered pair is indeed a solution. For example, if we have the ordered pair (8, 4) and the equation equation you would replace x with 8 and y with 4, and check if both sides of the equation are equal.

The substitution method is a technique where we replace variables with specific values to determine if a certain condition holds true. In linear equations, this involves inserting the values from an ordered pair directly into the equation.
Substitution is straightforward:

• Take each component of the ordered pair and substitute them into the equation for the corresponding variables.
• Simplify the equation to see if the result fits the equation's conditions.

For instance, with the pair (8, 4) and equation equation, you substitute by plugging 8 in place of x and 4 for y. This action transforms the equation into a simple arithmetic expression that can be evaluated to verify the solution.

Arithmetic operations consist of basic mathematical procedures like addition, subtraction, multiplication, and division. These operations are crucial when you substitute values into an equation.
After substituting an ordered pair into an equation, you often need to perform arithmetic operations to simplify the expression and verify if the substitution works:

• First, handle any multiplication or division operations.
• Next, proceed with addition or subtraction.

In our case, after substituting (8, 4) into the equation equation, you would multiply term and then add result to check if both sides equal right. If they do, this signals that the ordered pair is a valid solution. / By following these steps, arithmetic operations help confirm whether the ordered pair satisfies the given equation.