Definition:Consistent Simultaneous Equations/Inconsistent
< Definition:Consistent Simultaneous Equations(Redirected from Definition:Inconsistent Simultaneous Equations)
Jump to navigation
Jump to search
Definition
A set of equations is described as inconsistent if and only if they are not consistent
That is, there exists no set of values for its variables such that all the equations are satisfied.
Examples
Arbitrary Example $1$
Consider the simultaneous equations:
| \(\ds x + y\) | \(=\) | \(\ds 10\) | ||||||||||||
| \(\ds x + 2 y\) | \(=\) | \(\ds 15\) |
These are satisfied with the values:
| \(\ds x\) | \(=\) | \(\ds 5\) | ||||||||||||
| \(\ds y\) | \(=\) | \(\ds 5\) |
and so are consistent.
Arbitrary Example $2$
Consider the simultaneous equations:
| \(\ds x + y\) | \(=\) | \(\ds 10\) | ||||||||||||
| \(\ds x + y\) | \(=\) | \(\ds 15\) |
These cannot be satisfied by any pair of values for $x$ and $y$.
Hence they are inconsistent.
Also see
- Results about consistent simultaneous equations can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): consistent: 1.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): inconsistent equations
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): consistent: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): inconsistent equations