Overview
On this page, we discuss how to use the method of elimination to solve a system of two linear equations with two variables.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Solve a linear system of two equations with two variables by adding or subtracting one equation from another to produce an equation containing only one variable.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Understand how to recognize when a linear system has no solutions or infinitely many solutions when solving by elimination, and what this means about the the graphs of the two linear equations.
To prepare for class
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Watch the following video (by Tyler Wallace) which shows how to solve a system of linear equations where the two coefficients for a particular variable add to zero by adding both sides of the equations:
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Watch the following video (by Tyler Wallace) which shows how to solve more general systems of linear equations by first multiplying an equation by an appropriate constant before adding or subtracting both sides of the equations:
After class
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Watch the following video (by DV Math) which shows more examples of solving systems of equations using the elimination method, with the last two examples illustrating how to recognize when a system has no solutions, or infinitely many solutions:
