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Questions and Answers
What is a system of linear equations?
What is a system of linear equations?
- A set of two or more linear equations (correct)
- An equation with one variable
- A method for solving inequalities
- A single linear equation
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?
What is a Coefficient?
What is a Coefficient?
A system of linear equations can have no solution.
A system of linear equations can have no solution.
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.
What is a Linear Inequality?
What is a Linear Inequality?
What is a system of linear inequalities?
What is a system of linear inequalities?
What are the solutions of a system of linear inequalities?
What are the solutions of a system of linear inequalities?
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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.
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