Substitution and evaluating expressions

When studying "Evaluating expressions with two variables," focus on the following key points:

1. Understanding Variables: Recognize that variables represent unknown or variable quantities, often denoted by letters such as $x$ and $y$.

2. Substituting Values: Learn how to substitute specific numerical values for the variables in an expression. For example, if $x = 2$ and $y = 3$, in the expression $3x + 2y$, you would calculate $3(2) + 2(3)$.

3. Order of Operations: Apply the order of operations (PEMDAS/BODMAS) correctly when evaluating expressions. This includes handling parentheses, exponents, multiplication and division (left to right), and addition and subtraction (left to right).

4. Evaluating Multiple Expressions: Practice evaluating multiple expressions with the same variables simultaneously to reinforce understanding.

5. Interpreting the Results: Be able to interpret what the evaluated expression signifies in a given context, especially in word problems.

6. Using Tables or Graphs: Explore how to represent relationships between the variables through tables or graphs for better visualization.

7. Practice Different Combinations: Work on different combinations of values for the variables to see how changes affect the outcome of the expression.

By mastering these points, you will effectively evaluate expressions that involve two variables.

When studying "Evaluating expressions with two variables: fractions & decimals," focus on the following key points:

1. Understanding Variables: Variables represent unknown values and can take on different numerical values, typically denoted by letters like $x$ and $y$.

2. Evaluating Expressions: Substitute the values of the variables into the expression correctly. For example, if you have an expression like $3x + 4y$, and $x = 2$ and $y = 1$, substitute to get $3(2) + 4(1)$.

3. Working with Fractions: Be comfortable with adding, subtracting, multiplying, and dividing fractions. Remember to find a common denominator when adding or subtracting.

4. Working with Decimals: Know how to perform arithmetic operations with decimals. Align decimal points when adding or subtracting, and be careful with place values in multiplication and division.

5. Order of Operations: Apply the correct order of operations (PEMDAS/BODMAS) when evaluating expressions, especially when both fractions and decimals are involved.

6. Combining like terms: If your expression has like terms, simplify them appropriately before performing any calculations.

7. Finalizing Answers: After evaluating an expression, be sure to express your answer in the simplest form possible, whether as a fraction or decimal.

By mastering these points, you'll be well-equipped to evaluate expressions with two variables effectively.