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.
some key topics that involve solving systems using the graphing method:
* geometry- solving various problems that involve systems
* linear programming
* word problems that involve two variables
* SAT and ACT exams
* more complex college prep math