Definition:Independent Equations

Definition

A set of simultaneous equations is independent if and only if it contains no dependent equations.

Examples

Arbitrary Example

Consider the set of simultaneous equations:

\(\text {(1)}: \quad\)

\(\ds x + y\)

\(=\)

\(\ds 3\)

\(\text {(2)}: \quad\)

\(\ds x + 2 y\)

\(=\)

\(\ds 6\)

Equations $(1)$ and $(2)$ are independent because the only $\tuple {x, y}$ which satisfies both equations is $\tuple {0, 3}$.

Also see

• Definition:Dependent Equations

• Results about independent equations can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): dependent equations
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): independent equations
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): dependent equations
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): independent equations