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7 - Systems of Linear Equations

As covered in Chapter 5, a Linear Equation is the relationship between two first degree variables. When you are presented with more than one it is called a System of Linear Equations, or simply a Linear System. The solution for a Linear System is the point(s) which satisfy all equations in the system. There are 3 types of solutions: unique, none, infinite. Unique solutions are those where there is a single point that will satisfy both, graphicly this is when the two lines have different slopes and thus intersect at a specific point. The none, or null solution is when there is no points that will satisfy all equations, graphicly this is when the two lines are parallel (same slope) and as such never intersect. The infinite solution is when every point that satisfies one equation also satisfies the other(s), graphicly this is when the two lines coincide exactly. An example would be 4x + 2y = 12 and 6x + 3y = 18, both of which can be rewriten as y = -2x + 6, meaning they represent the same line.

This chapter will cover the various ways of finding the solution set to a Linear System, by graphing, substitution, or linear combination. The chapter then moves on to applications of Linear Systems and the special types (specificly those with either no or infinite solutions). The chapter closes with expanding the knowledge of Linear Systems as it applies to inequalities.