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Solving a System of Linear Equations in Two Variables - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

A system of linear equations is two or more equations that contain the same variables. A solutions to a system of equations are the point where the lines intersect. There are four methods to solving systems of linear equations: graphing, substitution, elimination and matrices. Solving systems of equations first shows up in Algebra I, but more complex applications occur in Algebra II.

Solving a system of linear equations in two variables, so if you remember a linear equation is basically just the equation for a line and when we're solving a system what we're looking at is two equations so we have two lines and we're trying to figure out where those two lines intersect and if they intersect at all okay so there's three ways that this can occur okay? We have two lines that could possibly intersect at a single point which means we're going to have one answer which will be a coordinate point xy say like 2, -4 something like that.
Another situation that could occur those lines could be parallel which means they're not going to have any intersection of those lines, they're not going to have any solution for where those two lines are equal to each other and lastly those two equations could be for the same exact line which means we'll have infinite points lying on either those lines that'll give us the solution, okay, and so what we're going to do is we're going to talk about each of these.
There's a number of different ways of solving these out, you can solve graphically and in Algebra 2 we typically don't do too much of that solving graphically basically what you do is you take one line you plot it you take another line you plot it and you'd see where they cross okay, so we know how to do that but it's not really going to give us a mathematical answer we're not really going to be able to find this point unless our graphs are completely precise which is sort of a waste of time so what we can do is do these algebraically and there's two ways that we have at our disposal, substitution which is when we solve for a variable and plug it in or elimination which is when we add or subtract the two equations in hopes of getting rid of one of out variables so.
Systems of linear equations, basically dealing with how lines intersect or don't intersect and we have a couple of ways of doing them namely substitution or elimination.

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