Can Gaussian Elimination Solve a System with Identical Equations?

[Biloon]

2x+3y+3z=7
2x+3y+3z=7
2x+3y+3z=7

Using Gaussian Elimination... is it possible to find the value of x,y,z with three similar equation?

 

[ice109]

absolutely not

 

[HallsofIvy]

Actually it is. Not ONE value of course, there are an infinite number of (x, y, z) triples that satisfy 2x+ 3y+ 3z= 7 and you really only have one equation. In 3 dimensions 2x+ 3y+ 3z= 7 is the equation of a plane. Any (x,y,z) point on that plane satisfies that equation (and so, all "three" of your given equations).

 

[JasonRox]

Haha, I was thinking the same thing.