Isolating a variable in a quadratic system

Proved

WorkbookSource.problem_57310

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

(1) $4x^2+7xy=7y+2$ (2) $4xy+7y^2=4x+2$ $x=1$ is not a solution and so first equation implies $y=\frac{2(1-2x^2)}{7(x-1)}$

Source: InternLM Lean-Workbook, record lean_workbook_57310 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_57310  (x y : ℝ)
  (h₀ : x ≠ 1)
  (h₁ : 4 * x^2 + 7 * x * y = 7 * y + 2)
  (h₂ : 4 * x * y + 7 * y^2 = 4 * x + 2) :
  y = (2 * (1 - 2 * x^2)) / (7 * (x - 1))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_57310; Apache-2.0

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