SOLUTION: (Please help I'm so Confused!!!) What is meant by a dependent system of linear equations and how does this differ from an independent system or an inconsistent system?
Algebra ->
Coordinate Systems and Linear Equations
-> SOLUTION: (Please help I'm so Confused!!!) What is meant by a dependent system of linear equations and how does this differ from an independent system or an inconsistent system?
Log On
Question 949341: (Please help I'm so Confused!!!) What is meant by a dependent system of linear equations and how does this differ from an independent system or an inconsistent system? Found 2 solutions by Zucchini, macston:Answer by Zucchini(70) (Show Source):
You can put this solution on YOUR website! If the lines or equations don't intersect, or there is no solution that fits the system of equations, it is inconsistent. If the system of equations show one line, like for example 1=1 for an equation, it is dependent. If it's just a regular system of equations where there is a solution for the system of equations, it's independent.
You can put this solution on YOUR website! A system of equations is consistent if it has at least one solution. There are two types:
TYPE 1:Independent system has exactly one solution. The graph of this system is intersecting lines.
Example:
y=2x+3
y=(-1/2)x+3
This system has exactly one solution, the intersection at point (0,3)
GRAPH OF CONSISTENT INDEPENDENT SYSTEM:
TYPE 2:Consistent Dependent systems have infinite solutions Their graphs are the same line. Examples of these are multiples of an equation.
Example:
y=2X-3
y=(4X-6)/2
GRAPH OF CONSISTENT DEPENDENT EQUATIONS:
This graph looks like one line because the lines overlap, so there are infinite solutions.
INCONSISTENT SYSTEMS HAVE NO SOLUTIONS (No common solution)
Examples of this are parallel lines.
y=2x+2
y=2x+6
GRAPH OF INCONSISTENT SYSTEM:
(
