Question 75364: Explain what it means to solve a system of linear equations?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! A linear equation represents a straight line on a graph.
A system of linear equations would be more than one line.
Let's say the system of linear equations represents two straight lins on a graph.
To solve such a system of linear equatins means to find the point (x, y) at which these two lines intersect.
If the two lines do indeed intersect, then you can find the point of intersection algebraically or by graphing the two lines and inspecting the graph to find the point of intersection. This is called a "consistent system".
If the two lines do not intersect, then there are two posibilities:
1) They are parallel, in which case, there is no point of intersection and thus, no solution to this system of equations. This is called an "inconsistent system".
2) The two lines are collinear (one lies on top of the other), in which case, there is an infinite number of solutions because any point that lies on one of the lines will also lie on the other line. This is a "consistent system" and the equations are "dependent equations">
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