How to Solve Homogeneous Quadratic Equations: x²−xy+7y²=27, x²−y²=15 & x/y + y/x = 17/4

In this lesson, we dive deep into How to Solve Homogeneous Quadratic Equations, using real examination-style questions that strengthen your problem-solving skills in algebra and simultaneous equations.

This lesson is a continuation of our series on Linear–Quadratic & Homogeneous Methods, perfect for university students, engineering students, high-school learners, and mathematics enthusiasts all around the world.

🔍 What You Will Learn in This Live Session

We will break down, step by step, how to solve the following quadratic equation systems:

(i) 𝑥^2−𝑥𝑦+7𝑦^2=27,
𝑥^2−𝑦^2=15
(ii) 𝑥/𝑦+𝑦/𝑥=17/4, x^2-4xy+y^2=1

You will learn:
✔ How to identify homogeneous quadratic equations
✔ How to apply substitution using
y=mx
✔ How to transform the equations into solvable forms
✔ How to solve linear–quadratic pairs efficiently
✔ How to interpret solutions in real-world mathematics context

🎯 Who Is This Session For?

This live session is designed for:
✔ University & college students
✔ Engineering and science students
✔ High school & A-Level learners
✔ Teachers, tutors, and mathematics lovers globally
✔ Anyone preparing for competitive exams or entrance tests

🧠 Why This Lesson Is Important
Homogeneous quadratic equations appear in:
Algebra
Engineering Mathematics
Calculus foundations
Physics
Applied mathematics
Exam questions at all levels
Mastering these techniques improves your reasoning, mathematical fluency, and exam performance.

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