SOLUTION: hello can someone please help me with this problem: Give an example of an identity involving a system of three equations in three unknowns. please help me with this problem

Question 324257: hello can someone please help me with this problem:
Give an example of an identity involving a system of three equations in three unknowns.
please help me with this problem! (:
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
An identity would be like three equations that are actually "identically" the same! How about

x+y+z=5
2x+2y+2z=10
3x+3y+3z=15

All three equations are actually the same! This would be an identity, right???

An additional thought comes to mind. Each of these equations represents a PLANE in 3-dimensions.

Did you notice that in the second equation, if you divide both sides by 2, you get the same equation as the first equation. Likewise, if you divide both sides of the third equation by 3, then you get exactly the same equation. So, the three equations that I gave as my example all represent exactly the SAME plane. Each equation is IDENTICALLY the same, so that's why we call this an IDENTITY.

Any solution of one equation will automatically be a solution of the other two equations as well.

Dr. Robert J. Rapalje, Retired
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