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Exploring the Expression (2x - 5y)
The expression (2x - 5y) is a simple algebraic expression that involves two variables, x and y, and two constants, 2 and -5. Let's delve into its various aspects and applications.
What it Represents
At its core, (2x - 5y) represents a linear combination of the variables x and y. This means that the expression takes the value of x, multiplies it by 2, and then subtracts 5 times the value of y.
For example, if x = 3 and y = 2:
- 2x = 2 * 3 = 6
- 5y = 5 * 2 = 10
- (2x - 5y) = 6 - 10 = -4
Applications
The expression (2x - 5y) has wide applications in various areas, including:
- Algebra: It is used in solving equations, simplifying expressions, and understanding the concept of linear relationships.
- Geometry: It can represent the equation of a line, where x and y represent the coordinates of a point on the line.
- Physics: The expression can be used to represent quantities like displacement, velocity, or force, depending on the context.
- Economics: It can be applied to models of supply and demand, where x and y represent quantities of goods or services.
Manipulating the Expression
You can perform various operations on the expression (2x - 5y) using the rules of algebra. Here are some examples:
- Adding or subtracting other expressions: You can add or subtract other expressions involving x and y to the original expression. For instance, (2x - 5y) + (3x + 2y) would result in 5x - 3y.
- Multiplying by a constant: Multiplying the entire expression by a constant simply scales the result. For instance, 3(2x - 5y) would become 6x - 15y.
- Factoring: In some cases, you can factor out a common factor from the expression. For example, (2x - 5y) can be factored as (2)(x - 2.5y).
Conclusion
The expression (2x - 5y) is a fundamental building block in mathematics and various fields. It represents a simple yet powerful concept of linear combination that has wide applications in solving problems and understanding relationships between variables.