I appreciate your answer very much, but still there are six variables!
In fact,these variables are actually the coordinates of a body in space: (x1,y1,z1),(x2,y2,z2)
It would help a lot if you put the question into its context. WHY do you want to eliminate three variables? WHICH should they be, if it matters? And if, as it appears, you showed us one step in some larger explanation of something, what did they do next?
Please help me how I could eliminate 3 variables in the following simultaneous equations so that they become in 3 variables instead of 6:
View attachment 15024
I do see that in saying "eliminate 3
variables" (which JeffM did, reducing to three
other variables), you misquoted the problem, which explicitly says to "eliminate 3
coordinates", implying that changing to new variables is not what they have in mind. But we don't know why the former is not acceptable, because we don't know the goal.
EDIT: After writing that, I searched for a phrase from the image, and found it appears to be from this book:
The series of texts on Classical Theoretical Physics is based on the highly successful series of courses given by Walter Greiner at the Johann Wolfgang Goethe University in Frankfurt am Main, Germany. Intended for advanced undergraduates and beginning graduate students, the volumes in the series...
books.google.com
Nothing is shown of how they eliminate coordinates, but the goal is simply to show that there are three degrees of freedom. Doesn't what JeffM did accomplish that goal?