# Solving Linear Systems

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Solving linear systems requires creating a table for both X and Y variables and graphing the equation accordingly. Visualize how a linear system works with examples from a tutor in this free video on math.

Part of the Video Series: Math Lessons
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## Video Transcript

Hi, my name is Samir Malik, I'm a tutor for middle school and high school students in the Austin Texas area and today I'm going to be describing how to solve linear systems. Now, with linear systems, basically what you need to have is a graph with both X and Y coordinates and you have the point for which includes both X and Y variables. When you have that point, you would solve for the X and you would solve for the Y at the same time. You would create a table and then you would graph accordingly to solve for that particular linear system. So, I'd like to go ahead and illustrate this by showing you an example of a point and then going ahead and just graphing it for you as well. So you have the equation "Y equals three X minus five," let me go ahead and draw our table first with our X axis and Y axis, where X can be zero, Y is negative five and X is one, Y is negative two, X is two and Y is one. And then we go ahead and graph it on our coordinate graph, which we have X is zero, Y is negative five, so negative one, negative two, negative three, negative four, negative five. And we have X is one, and Y is negative two. So, I'm sorry, X is zero, Y is negative five, so one, two, three, four, five, one, two, three, four, five, negative five. So this would be the point for zero, negative five. Then we have one, negative two, so one, negative two would be the next point, which is one, negative two, and the third point would be two, one, which is two and then one, here, two for the X value, one for the Y value. And we, we can go ahead and see here, that we have this line here which we've created. And, this is basically how we solve the linear system, because we had the equation, Y equals three X minus five, we draw our table with X and Y values, and then we go ahead an put this on a coordinate plane to illustrate how this linear system is solved. So, to summarize, to solve the linear systems, we basically have to have the equation, then we draw our table, and then we graph accordingly, and that will help us visualize to see how the linear system actually works.

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