Podcast
Questions and Answers
What is a system of linear equations?
What is a system of linear equations?
What is the Graphing Method used for?
What is the Graphing Method used for?
To solve a system of linear equations by graphing both equations.
Describe the Substitution Method.
Describe the Substitution Method.
A method that solves one equation for one variable and substitutes it into the other equation.
What does the Elimination Method involve?
What does the Elimination Method involve?
Signup and view all the answers
What is a Coefficient?
What is a Coefficient?
Signup and view all the answers
A system of linear equations can have no solution.
A system of linear equations can have no solution.
Signup and view all the answers
Infinite solutions occur when the two equations in a system are the same line.
Infinite solutions occur when the two equations in a system are the same line.
Signup and view all the answers
What is a Linear Inequality?
What is a Linear Inequality?
Signup and view all the answers
What is a system of linear inequalities?
What is a system of linear inequalities?
Signup and view all the answers
What are the solutions of a system of linear inequalities?
What are the solutions of a system of linear inequalities?
Signup and view all the answers
Study Notes
System of Linear Equations
- A system of linear equations consists of two or more linear equations that can be solved simultaneously.
Methods for Solving Linear Equations
- Graphing Method: Solving systems by graphing equations on a coordinate plane and finding their intersection point.
- Substitution Method: Involves solving one equation for a variable and substituting that expression into the other equation to solve for the remaining variable.
- Elimination Method: Involves adding or subtracting the equations to eliminate one variable, allowing for the solution of the remaining variable.
Key Definitions
- Coefficient: The numerical factor multiplied by a variable in an equation, indicating its relationship to the variable.
- No Solution: Occurs when no ordered pair can satisfy both equations, illustrated by parallel lines with the same slope but different y-intercepts.
- Infinite Solutions: Happens when an infinite number of ordered pairs satisfy both equations, represented graphically by coincident lines (the same line).
Linear Inequalities
- A linear inequality is a statement similar to a linear equation but uses an inequality symbol instead of an equal sign.
- System of Linear Inequalities: Consists of two or more linear inequalities that can be analyzed together.
Solutions of Linear Inequalities
- Solutions of a system of linear inequalities represent the overlapping region where both inequalities are true, shown by the area where the shaded regions intersect in a graph.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of key terms related to systems of linear equations and inequalities. This quiz features vocabulary flashcards designed to help you understand essential concepts like the graphing method and substitution method. Perfect for students looking to enhance their math vocabulary!
