# Consistent Equations

## consistent equations

[kən′sis·tənt i′kwā·zhənz]
(mathematics)
Two or more equations that are all satisfied by at least one set of values of the variables.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Consistent Equations

a system of equations such that there exists a set of values of the variables that satisfies each equation. For example, the equations x2 + y2 = 13 and x + y = 5 are consistent, since they are satisfied by the values x = 2 and y = 3. The equations x2 + y2 = 13 and 2x2 + 2y2 = 5, on the other hand, are inconsistent. Geometrically, the consistency of a system of equations means that the sets of points representing the equations share a common point.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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