Questions and Answers
What is a system of linear equations?
Define an inconsistent system.
A system where there is no solution because the lines are parallel.
What determines the solution of a system of linear equations?
The intersection of the lines on the xy-plane.
What is a consistent independent system?
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A system of linear equations consists of equations that graph as curved lines.
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What is the solution of a system of linear inequalities?
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How should you graph a system of linear inequalities?
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Study Notes
System of Linear Equations
- A system consists of multiple linear equations considered simultaneously.
- Simplest form includes two equations with two variables.
Inconsistent System
- Defined as a system with no solution due to parallel lines.
- Infinite solutions arise in a dependent system, which represents the same line in different forms.
Solution of a System of Linear Equations
- Solutions correspond to the intersection points of lines on the xy-plane.
- Results can be a line, a single point, or no solution, indicated by the empty set.
Consistent Independent System
- Characterized by having exactly one solution.
- If a consistent system has infinite solutions, it is termed dependent.
- Inconsistent systems are typified by having no solutions, represented graphically as parallel lines.
Solution of a System of Linear Inequalities
- Solutions are ordered pairs satisfying all inequalities in the system.
- Each inequality's graph is plotted, with the applicable half-plane shaded to represent the solution set.
Graph of a System of Linear Inequalities
- Similar to the previous definition, focusing on the graphical representation.
- Each line is graphed sequentially, and the region that satisfies the inequalities is shaded.
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Description
Test your knowledge of key concepts from Algebra Chapter 6 with these flashcards. This quiz covers systems of linear equations, inconsistent systems, and solutions to systems of equations. Perfect for anyone looking to reinforce their understanding of algebraic principles.
