Linear systems (2 and 3 unknowns)
Substitution, elimination, GDC matrix solver.
2Γ2 systems. Use elimination or substitution.
3Γ3 systems. On Paper 1 (no calc), use elimination/substitution. On Paper 2, the GDC's matrix solver is fastest β but you must show the matrix set-up.
Worked example (3Γ3). Solve:
From first two: add β . From first: .
From first and third: subtract β . Then .
Check in second: β.
Three-variable systems with no unique solution:
- Inconsistent (no solution): equations contradict.
- Dependent (infinite solutions): equations are linearly dependent.
Both occur in HL Paper 3 problems where parameters are varied.
- 2Γ2: substitution or elimination.
- 3Γ3: elimination chains; GDC matrix on Paper 2.
- Check by substituting into the original equations.