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**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.

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

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**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.

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**Ex 1. Substitution Method**

Find all solutions to the system using substitution.

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**Ex 2. Find all solutions using substitution.**

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Class Work Find all solutions using substitution.

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**Ex 3. Find all solutions using elimination.**

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**Ex 4. Find all solutions using elimination.**

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Class Work Find all solutions using elimination. 3.

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**Systems of Linear Equations**

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

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

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

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

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HW p odd, p all

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