Chapter 7 · Test 2
Systems of Linear Equations
Substitution, elimination, rank, and economic equilibrium systems.
What you will learn
- Solve a two-equation system
- Solve a linear market system
- Recognize a unique linear solution
Reasoning habits that help
- Elimination combines equations so one unknown disappears, leaving a one-variable equation.
- A market-clearing model is a system because price and quantity must satisfy demand, supply, and equilibrium simultaneously.
- Nonsingularity, a nonzero determinant, invertibility, and uniqueness are equivalent for a square coefficient matrix.
Where economists use these methods
- Linear systems solve simultaneous economic relationships such as sector balances, prices, and resource constraints.
- Market systems jointly determine equilibrium price and quantity from demand, supply, and clearing conditions.
- Uniqueness tells economists whether a model produces one determinate prediction or permits multiple outcomes.