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I see what you are doing. Remember, Sage is Python too! So x is still x. Just because you showed a solution doesn't mean that x was actually assigned to 1. If you want that, you'll have to explicitly say so. There are a few ways to do this, but

sage: sols = solve([eq1, eq2, eq3], x, y, z,solution_dict=True)
sage: v = x.subs(sols[0])
sage: v
sage: x

is one way. Notice that here x is still x and v has your solution.

Let us know if this answers the question you have.