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Math - System of Two Equations










































2x + 2y = 2
6x + 6y =6

determine whether the system is consistent, inconsistent or dependent?

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Nov 13, 2011
Inconsistent & Consistent Linear Systems
by: Staff

Question:

2x + 2y = 2
6x + 6y =6

determine whether the system is consistent, inconsistent or dependent?



Answer:

2x + 2y = 2

6x + 6y =6


First, some definitions:

Inconsistent linear systems: No solutions at all. Graphically, inconsistent systems are parallel lines.

Consistent linear systems: A consistent system has at least one solution.

There are two categories of Consistent Systems:

1) Dependent Systems (also called underdetermined systems): there are an infinite number of solutions. There is not enough information to find a single, unique solution. Graphically, dependent systems are the same line.

2) Independent Systems (also called uniquely determined systems): Independent systems have "one"solution. Graphically, the solution is the point where the two lines described by the equations intersect.


Your two equations form a "consistent" system because there is a least one solution.

Your two equations are also a "dependent" system because the second equation is merely three times the first equation. Graphically your two equations are the same line. There are an infinite number of solutions.


The final answer to your question is: system is consistent and dependent.






Thanks for writing.

Staff
www.solving-math-problems.com


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