1. Systems of Linear Equations
Systems of Linear Equations by Substitution
Opening Routine
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales
the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on
the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen
ticket and the price of a child ticket.

2. Systems of Linear Equations
Systems of Linear Equations by Substitution
Opening Routine
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

3. Systems of Linear Equations
Systems of Linear Equations by Substitution
Opening Routine

4. Topic V: Systems of Linear Equations

5. Systems of Linear Equations
Systems of Linear Equations by Elimination
Objective: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Essential Question: How do you use elimination to solve a system of linear equations?

6. Systems of Linear Equations
Systems of linear equations by elimination
Vocabulary
System of linear equations: Two or more linear equations form a system of linear equations.
Solution of a system: Any ordered pair that makes all the equations of system true is a solution of a system of linear equations.
Consistent system: A linear system of equations is consistent if there is at least one set of values that satisfies every equation in the system.

7. Systems of Linear Equations
Systems of linear equations by elimination
Vocabulary
Inconsistent system: A system of equations that graphs as parallel lines, there can be no solution. This is called an "inconsistent" system of equations, and it has no solution.
Independent system: A linear system that has exactly one solution is called a consistent independent system. Consistent means that the lines intersect and independent means that the lines are distinct.

8. Systems of Linear Equations
Systems of linear equations by elimination
Vocabulary
Dependent system: Linear systems composed of lines that have the same slope and the y-intercept are said to be consistent dependent systems. Consistent dependent systems have infinitely many solutions since the lines coincide.
Equivalent systems: Two linear systems are "equivalent" if they have the same solution.

9. Systems of Linear Equations
Systems of linear equations by elimination
In the elimination method, you can use the Addition or Subtraction Properties of Equality to add or subtract equations in order to eliminate a variable in the system.

10. Systems of Linear Equations
Systems of linear equations by elimination

11. Systems of Linear Equations
Systems of linear equations by elimination

12. Systems of Linear Equations
Systems of linear equations by elimination

13. Systems of Linear Equations
Systems of linear equations by elimination

14. Systems of Linear Equations
Systems of linear equations by elimination

15. Systems of Linear Equations
Systems of linear equations by elimination
Guided Practice – WE DO
The sum of two numbers is 20. When the larger number is subtracted from twice the smaller number, the difference is 4. What are the numbers?

16. Systems of Linear Equations
Systems of linear equations by elimination
Guided Practice – WE DO

17. Systems of Linear Equations
Systems of linear equations by elimination
Independent Practice - YOU DO
Worksheet
“Solving Systems of Equations by Elimination” Exercises 1 – 16

18. Systems of Linear Equations
Systems of linear equations by elimination
Closure
Essential Question: How do you use elimination to solve a system of linear equations?

19. Systems of Linear Equations
Systems of linear equations by elimination
Homework
Complete Worksheet
“Solving Systems of Equations by Elimination” Exercises 1 – 16