Solving Systems of Two Equations

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Presentation transcript:

Solving Systems of Two Equations Algebra II with Trigonometry Mr. Agnew

Essential Stuff Essential Question Essential Vocabulary How do you solve a system of equations? Essential Vocabulary System of Equations Solution Substitution and Elimination

Systems of Equations A system of equations is two or more related equations. The solution to a system of equations is a point. Some systems will have one solution (a point) while others will have no solution or infinitely many solutions.

Methods of Solving There are three methods to solve a system of equations: Graphing Substitution Elimination

Solving Systems Graphing Different Slopes: the lines intersect so there is one solution.

Solving Systems Graphing Same Slope and Different Y-Intercepts: The lines do not Intersect so there are No Solutions. They are parallel!

Solving Systems Graphing Same Slope and Same Y-Intercept: The lines are the same so there are Infinitely Many Solutions.

Solving Systems SUBSTITUTION Isolate a variable in one equation and plug it into the other equation. Examples

Solving Systems ELIMINATION Examples Add the two equations together to eliminate one of the variables. You may need to multiply the equations by a number to help eliminate a variable. Examples

Homework Homework 3.3: Solving Systems of Two Equations