Section 9.2 Systems of Equations

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Presentation transcript:

Section 9.2 Systems of Equations Objectives: To solve systems using substitution. To solve systems using elimination. To put systems into triangular form so they can be solved with back substitution.

Systems of Equations. A system of two linear equations in two variables has the form where a, b and c are real numbers.

For a system of linear equations in two variables, exactly one of the following is true. The system has exactly one solution. The system has no solution. The system has infinitely many solutions.

Ex 1. Substitution Method Find all solutions to the system using substitution.

Ex 2. Find all solutions using substitution.

Class Work Find all solutions using substitution.

Ex 3. Find all solutions using elimination.

Ex 4. Find all solutions using elimination.

Class Work Find all solutions using elimination. 3.

Systems of Linear Equations Here are two examples of systems of linear equations in three variables. System of Linear Equations System in Triangular Form

Ex 5 Use back-substitution to solve the triangular system.

Ex 6. Use back-substitution to solve the triangular system.

Class Work Use back-substitution to solve the triangular system. 4. 5.

HW p 649 7 - 25 odd, p 657 6 -10 all