To describe: three different possibilities that may occur while graphing a given system with example and solutions.
Answer to Problem 3CFU
Possibility 1: Intersecting lines. All independent system has only one solution. Example:
Possibility 2: Parallel lines. All independent system has only one solution. Example:
Possibility 3: Coinciding lines. All dependent system has infinite solutions. Example:
Explanation of Solution
Given information:
The possibilities that may occur while graphing a system of two linear equations
Calculation:
The three possibilities that may occur while graphing a system of two linear equations are as follows:
- The graph of the equations is the lines that intersect with each other. All independent system has only one solution and therefore falls under this category. The example for this possibility is shown below.
- The graph of the system of equations consisting of two parallel lines. This system of equation has no solution because the parallel lines do not intersect each other. All inconsistent system of equation falls under this category. The example for this possibility is shown below.
- The graph of the system of equations consisting of two coinciding lines. All dependent system of equation having infinite solutions falls under this category. The example for this possibility is shown below.
Chapter 2 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Additional Math Textbook Solutions
Precalculus (10th Edition)
Calculus: Early Transcendentals (2nd Edition)
Calculus and Its Applications (11th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Thomas' Calculus: Early Transcendentals (14th Edition)
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