Can Gaussian Elimination Solve a System with Identical Equations?

AI Thread Summary
Gaussian elimination cannot yield a unique solution for a system with identical equations, such as 2x + 3y + 3z = 7 repeated three times. Instead, it results in an infinite number of solutions, as all points (x, y, z) on the corresponding plane satisfy the equation. The discussion emphasizes that despite having three equations, they represent the same plane in three-dimensional space. Thus, the system does not provide distinct values for x, y, and z. The key takeaway is that identical equations lead to a single plane with infinitely many solutions.
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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?
 
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absolutely not
 
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).
 
Haha, I was thinking the same thing.
 
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