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# Systems of Linear Equations Overview

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### What is an independent system?

A system that has exactly one solution.

### What is a dependent system?

A system that has infinite solutions.

### What is an inconsistent system?

A system that has no solution.

### What is a consistent system?

<p>A system that has at least one solution.</p> Signup and view all the answers

### When solving a system algebraically, how can you determine if the system has infinite solutions?

<p>The resulting equation will be a TRUE STATEMENT, for example, 7=7.</p> Signup and view all the answers

### When solving a system algebraically, how can you determine if the system has no solution?

<p>The resulting equation will be a FALSE STATEMENT, for example, 2=5.</p> Signup and view all the answers

### When solving a system algebraically, if the resulting statement is 0 = 0, how does the graph look and how do you classify the system?

<p>Coinciding lines. Consistent. Dependent.</p> Signup and view all the answers

### When solving a system algebraically, if you're able to solve for x, how does the graph look and how do you classify the system?

<p>The lines intersect in exactly one point. Consistent. Independent.</p> Signup and view all the answers

### When solving a system algebraically, if your resulting equation is -2=2, how does the graph look and how do you classify the system?

<p>Parallel lines. Inconsistent.</p> Signup and view all the answers

### Give an example of a dependent system.

<p>y = 2x + 3 and -3 + y = 2x.</p> Signup and view all the answers

## Study Notes

### Classifying Systems of Linear Equations

• Independent System: Contains exactly one solution; represented visually by two lines that intersect at a single point.

• Dependent System: Has infinitely many solutions; shown graphically as coinciding lines, indicating they are the same line.

• Inconsistent System: Results in no solutions; depicted by parallel lines that never intersect.

• Consistent System: At least one solution exists; this term encompasses both independent and dependent systems.

### Solving Systems Algebraically

• Infinite Solutions Determination: If the resulting equation is a TRUE STATEMENT (e.g., 7=7), it indicates infinite solutions.

• No Solution Determination: If resolving leads to a FALSE STATEMENT (e.g., 2=5), it signifies that the system has no solutions.

### Graphical Representations and Classifications

• Resulting Equation: 0 = 0: Indicates coinciding lines; classified as consistent and dependent due to infinite solutions.

• Solving for x Successfully: Represents lines intersecting at exactly one point, classifying the system as consistent and independent.

• Resulting Equation: -2 = 2: Represents a contradiction; visual representation shows parallel lines, classifying it as inconsistent.

### Example of a Dependent System

• Dependent System Example:
• Equation 1: y = 2x + 3
• Equation 2: -3 + y = 2x
• Both equations represent the same line, confirming the nature of dependence.

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## Description

This quiz covers the classification of systems of linear equations including independent, dependent, and inconsistent systems. It also explores solving systems algebraically and graphical representations of these equations. Test your understanding of the fundamental concepts and terminology related to linear equations.

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