Can You Solve This System of Radical Equations?

Can you find x and y from this challenging radical system?
Given: √(x-1) + √(y-1) = 8 and √(x+7) + √(y+7) = 10, Find x and y
This problem features two equations with shifted radical expressions that looks incredibly complex! But there's a strategic approach using substitution or recognizing the relationship between the shifts. The key is setting up new variables or manipulating the equations to reveal the connection between x and y.
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This problem teaches you:
✓ System of radical equations
✓ Strategic substitution techniques
✓ Recognizing shifted patterns
✓ Multi-equation problem solving
✓ Algebraic manipulation skills
Perfect for students preparing for:
• Math Olympiads IMO, AMC, AIME
• Competition mathematics
• Advanced Algebra and Pre-Calculus courses
• Anyone who loves challenging systems!
The solution requires clever substitution and yields clean integer values!
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