System of equations solved by multiple methods. Elimination: create like terms, add/subtract equations to eliminate variables. Substitution: express one variable in terms of other, substitute. Graphical: intersection point is solution. Key considerations: number of solutions (unique, none, infinite). Substitution best when coefficients are 1 or -1. Elimination efficient with aligned coefficients. Shortcut: use matrix form for quick visualization. Common traps: losing equations during manipulation, sign errors. Exam tips: match method to equation structure, verify final answer. Time-saving: identify simplest variable to eliminate first. Applications: mixture problems, break-even analysis. Augmented matrix approach: [a|b] notation. Always check solution consistency. Dependent equations produce infinite solutions (same line). Inconsistent systems have no solution (parallel lines). Practice recognizing system types by inspection.