Problem 20 - BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Question

\(x=-4, y=-\frac{5}{4}\)

Step-by-Step Solution

Answer

The evaluated variables are x = -4 and y = -1.25.

Step 1: Understanding expression 1

The first expression is \(x=-4\). This implies that 'x' is equal to -4.

Step 2: Understanding expression 2

The second expression is \(y=-\frac{5}{4}\). It signifies that 'y' is equal to -\( \frac{5}{4} \) or -1.25 if one converts the fraction into decimal.

Step 3: Putting it together

Now we have understood the values of the variables. The value of 'x' is -4 and 'y' is -1.25. There isn't any further calculations or interpretation required.

Key Concepts

Understanding Expressions

When tackling algebraic expressions, it's crucial to grasp the fundamental idea of what an expression is. An expression in algebra can include numbers, variables (symbols that stand for numbers), and operations (like addition or multiplication). In our example, we have two expressions: \(x = -4\) and \(y = -\frac{5}{4}\). Each part of the expression provides information about what the variable represents. Understanding this allows us to easily translate the "code" of algebra into understandable quantities.
This means whenever an expression is given, you're offered a value or a rule to plug into calculations or equations. Keeping this in mind will help you comprehend more complex algebraic problems as they arise. Also, remember: the more you practice, the more familiar these patterns will become.

Variable Assignment

Variable assignment is a crucial step in solving algebraic problems. It signifies associating a specific value with a variable—an unknown symbol represented by letters such as 'x' or 'y'. In the example expressions \(x = -4\) and \(y = -\frac{5}{4}\), 'x' and 'y' are variables. Here, their specific assigned values are -4 and \(-\frac{5}{4}\) respectively.

• This tells us that whenever we see 'x', we substitute it with -4.
• Similarly, 'y' should be substituted with \(-\frac{5}{4}\) in any equation or formula.

Understanding this allows seamless integration of different variables into equations, making complex equations manageable by operating through substitutions. This assignment process ensures clear communication and helps verify solutions through logical reasoning.

Fraction to Decimal Conversion

Converting fractions to decimals is a useful skill in mathematics that can make understanding and comparing numbers more straightforward. Consider the fraction \(-\frac{5}{4}\) from the previous example. To convert it into a decimal, you divide the numerator by the denominator:

• The numerator (-5) divided by the denominator (4) yields -1.25.

This conversion process is helpful as decimal numbers often provide a clearer picture, especially when conducting operations like addition or subtraction.
Remember, fractions represent parts of a whole, while decimals offer that same value in terms of tenths, hundredths, or thousandths. You simply perform the division to discover the decimal format. Moreover, understanding this conversion builds a bridge between different numerical representations, enriching your mathematical toolkit for problem-solving.