Systems of Equations: Inconsistent/Consistent; Independent/Dependent

When graphing systems of equations, you can figure out whether they are consistent or inconsistent.
If they are consistent, you then see whether they are independent or dependent.

(1) The differences


►If the lines are parallel to each other:
•there is no solution (There is no place of intersection - which would have been the solution, therefore no solution.)
•and they are inconsistent (have no points in common)
►If lines intersect:
•they have a solution such as (2, -4) or where ever they intersect, and that is what you write. "(2, -4)"
•they are consistent (have at least one point in common)
•and they are independent (of each other -- they go their own direction)
►If lines land in the same place, on top of one another:
•the solution is along the entire line - any and all points on the line will work as the solution, so you would say "entire line" or "infinite."  There is an infinite number of possible points along the entire line.
•they are consistent (have at least one point in common)
•they are dependent (do not go their own direction)

(2) Using substitution to tell the difference