MAT017 · Matrices & determinants · Classes 11–12
Cramer's rule
Cramer's rule solves a system with determinants: replace a column of A by the constants to get Dₓ or D_y, then divide by D = det A.
x = Dₓ/DCramer's rule
📐 Formula
x = Dₓ/D, y = D_y/D
✏️ Worked example
3x + 2y = 8, x − y = 1: D = −5, Dₓ = −10, D_y = −5, so x = 2, y = 1.
🌍 Where it is used
Quick exact solutions for small systems.
❓ Quick check
Cramer's rule fails when…
🏋️ Practice
EasyD = 4, Dₓ = 8. x?
Answer: 2
MediumSolve x + 2y = 5, 3x + 4y = 11 by Cramer.
Answer: x = 1, y = 2
ChallengeD for 2x + y, x + 3y?
Answer: 5