# Systems of Linear Equations

**Topics:**High school, Elementary algebra, Intersection

**Pages:**2 (508 words)

**Published:**March 15, 2005

There are three main methods of defining a system of linear equations. One way is called a consistent, independent solution. This essentially means that the system has one unique, definite solution. In this situation on a graph, a set of two equations and two variables would be solved as one single point where two lines intersect. It is much the same with three variables and three equations. The only difference is that the point is an intersection of three planes instead of two lines.

Additionally, there are situations where a system of linear equations could be described as consistent, dependent. These systems of linear equations have an infinite number of solutions where a general solution is used to substitute one or two variables for one other selected variable, and solves the other unknown variable or variables in terms of that selected one. Graphically when this system of linear equations is solved for two equations and two variables, the result is lines that coincide, or lay on top of each other, making any point on that line true for the system. A system with three equations and three variables would yield an answer that shows the three planes intersecting on a line or overlaying each other. When the system yields three planes intersecting on a line, all points on the line would make the systems true, and when planes coincide, all points on the coincidental planes would be correct when placed in the system for the variables....

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