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Section 9.2 Systems of EquationsObjectives: 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 MethodFind 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 EquationsHere 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.
HW p odd, p all
System of Equations A set of two or more equations with the same variables. To solve a system of equations means to find values for the variables in the.
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7.1 SOLVING SYSTEMS BY GRAPHING The students will be able to: Identify solutions of linear equations in two variables. Solve systems of linear equations.
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Systems of Equations Substitution Elimination Inequalities Systems of Inequalities Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500.
I can solve systems of equations by graphing and analyze special systems.
3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =
Matrix Solutions to Linear Systems. 1. Write the augmented matrix for each system of linear equations.
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