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# Chapter 3 linear systems

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• 1. Chapter 3 Linear Systems
3.1 Solving Systems Using Tables and Graphs
3.2 Solving Systems Algebraically
• 2. System of Equations
A system of equations is a set of two or more equations
A linear system consists of linear equations
A solution of a system is a set of values for the variables that makes all the equations true.
(usually an ordered pair)
Systems can be solved be various methods: graphing, substitution, and elimination
• 3. Solving a system by graphing
Write each equation in slope-intercept form
Graph each line
Find the point of intersection (this is your solution)
Check by substituting the values into both equations
• 4. Solve each system by graphing
• 5. Classifying Systems
A system of two linear equations can be classified by the number of solutions it has
A consistent systems has at least one solution
An independent system has one solution
A dependent system has infinitely many solutions
An inconsistent system has no solution
• 6. Without graphing, classify each system as independent, dependent, or inconsistent
Rewrite each equation into slope-intercept form
Compare the slopes and y-intercepts
Different slopes: independent system
Same slope and same y-intercept: dependent system
Same slope and different y-intercept: inconsistent
• 7. Without graphing, classify each system as independent, dependent, or inconsistent
• 8. Without graphing, classify each system as independent, dependent, or inconsistent
• 9. Solving Systems by Substitution
Solve one equation for one of the variables
Substitute the expression into the other equation and solve
Substitute the solution into one of the original equations and solve for the remaining variable
Check the solution
• 10. Solving Systems by Substitution
Use when it is easy to isolate one of the variables
• 11. Solving by Elimination
Rewrite both equations in standard form
Multiply one or both systems by an appropriate non-zero number (note you want one variable to drop out in the next step)