box% sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.5, Release Date: 2022-01-30                     │
│ Using Python 3.10.2. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
sage: R.<x0,y0,r> = PolynomialRing(QQ, order='lex')
sage: ideal(x0^2 + y0^2 - r^2, 2*x0 - 47, r - 10 - y0).groebner_basis()[-1]
r - 2609/80
sage: N(2609/80)
32.6125000000000
sage: