Solving Linear Systems by Graphing

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Presentation transcript:

Solving Linear Systems by Graphing 3.1 Algebra II

Steps Write all equations in the form y=mx+b Graph all equations The intersection of the lines is the solution to the system of equations

Example #1 Solve by graphing. Then check your answer algebraically. 3x-y=3 x+2y=8

Example #2 -x+4y=2 2x-3y=6

The systems in examples 1 and 2 have exactly one solution The systems in examples 1 and 2 have exactly one solution. However, it is possible for a system to have no solutions or infinitely many solutions. Same line= infinitely many solutions Parallel lines= no solutions

Example #3 2x-y=1 -4x+2y=-2

Example #4 x+2y=4 x+2y=1

Writing and Using a Linear System You are planning a 7-day trip to California. You estimate that it will cost $300 per day in San Diego and $400 per day in Anaheim. Your total budget for the trip is $2400. How many days can you spend in each city? Use a graph to find your answer.

Assignment Pg. 128-130 # 8-10, 14-18, 23-30, 35-38, 43-55 odd