Linear equations with two variables: ax + by + c = 0. Graphical representation: straight line on coordinate plane. Key methods: substitution, elimination, graphical. Substitution: solve one variable, substitute into other. Elimination: multiply equations to cancel variables. Shortcut: identify quick cancellation opportunities. Common traps: arithmetic errors in multiplying equations, sign mistakes. Exam tips: check solution in both equations, use consistent variable order. Time-saving: notice when coefficients already align. Applications: intersection problems, optimization scenarios. Consistency check: verify solutions work in both equations. Parallel lines have no solution (inconsistent), coincident lines have infinite solutions. Practice identifying system type quickly. Algebraic skills crucial: multiplication, addition, variable isolation.