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Chapter 1: Problem 1

If \(x\) and \(y\) are real numbers, then \((x, y)\) is an _____ pair of real numbers.

Short Answer

Expert verified
ordered

Step by step solution

01

Understanding the Problem

Identify what the given problem is asking. It asks for a term to describe the pair \(x, y\) where \(x\) and \(y\) are real numbers.
02

Identify Important Information

The key information is that \(x\) and \(y\) are real numbers and they form a pair.
03

Recall Definitions

Recall from algebra that a pair of values written in the form \( (x, y) \) is called an 'ordered pair'.
04

Conclusion

Therefore, \( (x, y) \) is an ordered pair of real numbers.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Real Numbers
Real numbers are all the numbers on the number line. They include all the rational numbers (like integers and fractions) and irrational numbers (like the square root of 2 or pi (蟺)).

Real numbers can be positive, negative, or zero.

In algebra, we often deal with real numbers in different equations and expressions. These numbers are fundamental in various math calculations and understandings.

In the given problem, both x and y are stated to be real numbers. This means they could be any number that can be plotted on a number line. Understanding this foundation helps in progressing through algebraic problems effectively.
Algebraic Expressions
Algebraic expressions are combinations of variables, numbers, and operations (like addition, subtraction, multiplication, and division).

For example, an expression like 2x + 3y - 2 is an algebraic expression.

When we combine variables such as x and y with real numbers through operations, we create expressions that can be simplified or solved.

In the exercise, x and y represent variables that are real numbers. The ordered pair (x, y) conveys a specific location in a coordinate plane, which is an essential part of math expressions and equations.
Coordinate Geometry
Coordinate geometry, or analytic geometry, is the study of geometry using a coordinate system. This system uses ordered pairs (x, y) to define points in a plane.

The first number x represents the horizontal position, and the second number y represents the vertical position.

Understanding ordered pairs is crucial in coordinate geometry. It allows us to solve geometric problems algebraically.

In our problem, the ordered pair (x, y) defines a point on the coordinate plane where both x and y are real numbers. This point's exact location is determined by the specific values of x and y, whether it be right/left for x or up/down for y.

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