SMO Junior · 2. Equations, systems and word problems
Solve linear equations and systems with parameters, use substitution while respecting the domain, turn word problems into equations, and handle cyclic nonlinear systems by comparing the unknowns.
Decide when a linear equation or system has one, none or infinitely many solutions.
Find a requested combination of unknowns by adding or subtracting equations.
Solve radical and rational equations by substitution, checking the domain and rejecting false roots.
Translate averages, rates and payments into equations and finish with integer conditions.
Prove uniqueness of solutions of a cyclic system with the largest-variable argument.