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Why do people call it a system when two lines intersect?
They do not. A set of lines can also be considered as a system of linear equations. But the fact that there is such a system does not mean that the lines intersect.
A system of equations of two or more parallel lines is called a what?
Inconsistent
What is the purpose of the coordination system?
To plot straight and curved lines on it in the form of equations
What the system of linear equation in two variabes which has no solution?
For two linear equations, they are equations representing parallel lines. (The lines must not be concurrent because if they are, you will have an infinite number of solutions.) For example y = mx + b and y = mx + c where b and c are different numbers are two non-concurrent parallel lines. The equations have no solution. With more than two linear equations there is much more scope. Unless ALL the lines meet at one point, the system will not have a solution. So a system consisting of equations defining the three lines of a triangle, for example, will not have a solution.
Describe a consistent independent system of linear equations?
The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.
