This section has the following videos:
- Lesson Video
- Example Set A Practice Problems (Video Solutions)
- Example Set B Practice Problems (Video Solutions)
- Example Set C Practice Problems (Video Solutions)
- DOWNLOAD the Practice Problem Worksheet Here (the videos below explain the solutions to the problems)
Knowing how to solve a system of linear equations is an absolute must for algebra students. There are four basic ways you can solve a linear system:
* graphing method ( not really practical – only used to teach the concept of solutions to a system)
* substitution method (learn it, love it, don’t forget it)
* elimination / linear combination method (learn it, love it, don’t forget it)
* solving systems using matrices ( important, know it however not as easy as the substitution method and the elimination method )
The main point that I’m making is invest in knowing how to solve systems- as you gain experience you’ll see that each method has it’s advantages…
Ok lets take a closer look at the graph of a linear system. Just to be clear a linear system is basically two lines. Now lets think- if we graph two lines what can happen?
* the lines can intersect- this means the system has a solution located at the point where the two lines cross.
* the lines are parallel- the lines never cross = system has no solutions.
* the lines are actually on top of one another = system has infinite (many) solutions.