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The substitution method is a crucial concept in algebra that helps in simplifying expressions like the one in our example. This method involves replacing the variables in an expression with their given numerical values.
For instance, in the expression \(-5y + z\), the variables \(y\) and \(z\) are replaced by the values -0.2 and 5.7, respectively. The expression transforms into \(-5(-0.2) + 5.7\).
This process makes the expression purely numerical, allowing us to perform calculations easily. Substitution is particularly useful for solving equations or evaluating expressions with specific values.

• Replace each variable in the expression with its assigned number.
• Rewrite the expression using numbers instead of variables.

By substituting, we simplify the problem, making it more manageable and less abstract.

The order of operations is fundamental when dealing with algebraic expressions, just as it is in arithmetic.
To evaluate an expression correctly, you need to perform operations in the right order. The standard order is captured by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Each part of this sequence indicates the priority of operations.
In our example \(-5(-0.2) + 5.7\), there aren’t any parentheses influencing operations inside expressions. We only need to multiply before adding as indicated:

• First, compute the multiplication: \(-5\times(-0.2)\), which equals 1.0.
• Then proceed to the addition: 1.0 + 5.7 gives 6.7.

Following the correct order ensures accurate results, avoiding errors in simplification and evaluation.

Variable evaluation refers to determining the numerical value of an expression by substituting variable values. It involves understanding what each variable represents and how they contribute to the solution.
To evaluate \(-5y + z\) with specific values, we substitute \(y = -0.2\) and \(z = 5.7\), converting the expression from a general algebraic form to a numeric expression \(-5\times(-0.2) + 5.7\).
By plugging in the numbers and simplifying, variable evaluation turns abstract expressions into numerical outcomes.

• Identify the values for each variable in the expression.
• Substitute those values into the expression.
• Simplify the expression following order operations.

This approach makes it possible to understand and predict the behavior or output of an expression under specific situations, emphasizing the practical application of algebra in real-world scenarios.