Simultaneous Equations

At A-Level you must solve simultaneous equations where one equation is linear and one is quadratic (or involves other non-linear terms). This extends the GCSE skill of solving two linear simultaneous equations. The Edexcel 9MA0 specification requires both algebraic and graphical understanding.

---

Linear Simultaneous Equations — Recap

Two linear equations with two unknowns can be solved by elimination or substitution.

Example: Solve 2x + 3y = 12 and x − y = 1.

By substitution:

• From the second equation: x = y + 1
• Substitute into the first: 2(y + 1) + 3y = 12
• 2y + 2 + 3y = 12
• 5y = 10, so y = 2
• x = 2 + 1 = 3
• Solution: x = 3, y = 2

By elimination:

• Multiply the second equation by 3: 3x − 3y = 3
• Add to the first: 2x + 3y + 3x − 3y = 12 + 3
• 5x = 15, so x = 3, then y = 2

---

One Linear, One Quadratic