A single equation in two unknowns has infinitely many solutions: to pin down just one, we need two equations that must hold simultaneously. A collection of equations of this kind is called a system. In this chapter we learn to solve linear systems in two unknowns with the substitution method and with Cramer’s rule, based on determinants. In the final part — a capsule beyond the standard syllabus, useful as a springboard for physics and computer science — we introduce matrix calculus (sum, product and inverse of matrices), writing a system in matrix form and Gauss’s elimination method for larger systems. The chapter closes with an economic application: the equilibrium price between demand and supply, modelled precisely as a system.
Sections
- Substitution method
- Cramer’s method
- An outline of matrix calculus
- Demand, supply and equilibrium price