Consistent and inconsistent equations: Difference between revisions

Revision as of 15:07, 17 May 2020

Revision as of 05:38, 16 June 2020

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has the three solutions (''x, y'') = (1, –1), (–1, 1), and (1, 1).

===Overde

===Overdetermined and inconsistent===

The system

:<math>x+y=3,</math>

:<math>x+ 2y= 7,</math>

:<math>4x+6y=21</math>

is inconsistent because the last equation contradicts the information embedded in the first two, as seen by multiplying each of the first two through by 2 and summing them.

The system

:<math>x^2+y^2=1,</math>

:<math>x^2+2y^2=2,</math>

:<math>2x^2+3y^2=4</math>

is inconsistent because the sum of the first two equations contradicts the third one.

==Criteria for consistency==