Now that we know what a linear equation is, what is allowed, what is not allowed for linear equation, we can talk about a entire set of linear equations, pretty much called a linear system. Let's say I had 2, X1 plus X2 squared equals 3, and I also had negative X1 minus X2 equals negative square root of 4. Instantly, we should already know that a squared X term is not allowed in a linear system, so hopefully you caught that. But if we erase that, we now have a perfectly fine set of linear equations. Here, what we want to know is, what are the X1 and X2 values that make both equations true? If you think about a linear system, a set of linear equations, and you graph them, we might have a different set of linear equations, Y1, Y2 axis. We're no longer dealing with this specific set of linear equations, we'll deal with something else hypothetical, where we deal with a Y1 and a Y2 variable. It doesn't matter, just different name for a variable. We might have the situation where one linear equation and another linear equation cross. The values of Y1 and Y2 that make both equations true is what we're looking for. In this graph, it's just the point at which they intersect. We have one solution here. These lines will never cross again, so we're guaranteed to only have one solution. Now, in a different situation, Y1, Y2, we might have it so that these lines are parallel. In this case, two parallel lines will never intersect. No point on either of these two lines will make both equations true. In this case, we would have no solution set. Of course there is a third situation. That is, that we have one line in which both equations are giving us that same line. Essentially we have two linear equations that are both saying the same thing. In that case, every point on either line, since they're the same line, would make both equations true. In this case, we would have infinite solutions. When it comes to linear systems, when it comes to solutions, or the entire set of solutions called the solution set, we only have three options. There's either no solution, they're parallel to each other, there's one solution, where they cross, or there's an infinite amount of solutions because essentially they're the same line.