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The substitution method is a fundamental technique in algebra that involves replacing variables in an expression with specific numerical values. In this exercise, we are given the values of the variables and asked to substitute them into an expression. For example, if our expression is \(9x - 6y\), and we're given that \(x = 9\) and \(y = -2\), our first step is to make these substitutions. This means replacing \(x\) with 9 and \(y\) with -2, transforming the expression into \(9(9) - 6(-2)\).
Substitution helps simplify the problem by converting an algebraic expression into an arithmetic one that is easier to handle. This technique is crucial for solving not only simple evaluations like this but also complex algebraic equations.
Always ensure the substitution is done methodically:

• Directly replace the variable with its given value.
• Double-check to avoid mistakes.
• Bar brackets can help make the operation more clear, especially if negative values are involved, as it prevents arithmetic errors.

Arithmetic operations are basic math functions that include addition, subtraction, multiplication, and division. In this evaluation task, understanding how to manipulate these operations is essential. After substituting the given values into the expression \(9(9) - 6(-2)\), the next step involves using these operations.
Firstly, perform the multiplications:

• Calculate \(9 imes 9\), which results in 81.
• Calculate \(-6 imes -2\), which results in 12. Here, it's important to remember that multiplying two negative numbers gives a positive product.

Arithmetic operations follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). So, after the multiplications, we proceed to subtraction, which brings us to the simplified form of the expression.

Expression evaluation is the process of computing the value of an algebraic expression after substituting any given values for its variables. Once the substitution and arithmetic operations are completed, as with our example, the original expression \(9x - 6y\) becomes the arithmetic statement \(81 - 12\).
Here, we carry out the subtraction, which is now straightforward:

• Subtract 12 from 81.
• The result is 69.

Evaluating expressions is a key skill in algebra, enabling students to verify whether a solution is correct or to see how variables interact in an equation. This is often the final step, where you piece together all the previous steps to get to the simplest form, ensuring accuracy at each stage.