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Eliminating variables from a system of equations?

I'm (very) new to Sage, but am confused about why I can't get it to solve a simple system like this:

var('x, y, z') eqns = [ x^2 + y^2 == z, x == y]

but solve(eqns, z) gives an empty list back instead of my desired z = 2y^2

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Eliminating variables from a system of equations?

I'm (very) new to Sage, but am confused about why I can't get it to solve a simple system like this:

var('x, y, z')
eqns = [ x^2 + y^2 == z, x == y]

y]

but solve(eqns, z) gives an empty list back instead of my desired z = 2y^2