Solving Systems of Linear Equations

A set of all points that satisfy all of the linear equations in the system

Substitution, Graphing, and Linear Combination

Methods to Find the Solution of a System of Linear Equations

A method to find the solution of a system of linear equations that involves: 
 - Solving for one variable in the first equation 
 - Substitute the solution into the second equation
 - Solve the second equation for the single remaining variable 
 - Plug the solution for that variable into the first equation and solve for the other variable

Substitution Method for Solving a Linear System of Equations (2 equations)

A method to find the solution of a system of linear equations that involves:
 - Plot the first equation. (If necessary, convert the form to slope intercept or point slope form)
 - Plot the second equation
 - Identify the intersection. This is the solution

Graphing Method for Solving a Linear System of Equations (2 equations)

A method to find the solution of a system of linear equations that involves:
 - Put both equations into general form (or preferred form)
 - Choose one variable to eliminate
 - Multiply one or both equations by appropriate factors so that both equations will have the same coefficient for that variable (though one may be negative)
 - Add or subtract the equations, so that one variable drops out, leaving the other in the equation
 -Solve for the variable in that equation
 - Plug the solution into either equation to solve for the second variable

Linear Combination Method for Solving a Linear System of Equations (2 equations)

- Null set (no solutions)
- One point
-Infinite number of points

Three Possible Cases for the Solution Set

The lines are parallel (do not intersect)

Graphical Meaning of a Null Solution Set to a Linear System

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Solving Systems of Linear Equations Flashcards

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