Topic 3 of 6
Systems & Inequalities
Solve simultaneous conditions, choose an efficient method, and describe whole solution regions instead of isolated numbers.
01Algebra · Decision guideGraphing, substitution, or elimination: which system method fits?Choose from the equation structure: graph when the intersection matters visually, substitute when a variable is already isolated, and eliminate when coefficients align.02Algebra · Method guideSolving systems by substitutionReplace one variable with an equal expression, solve the resulting one-variable equation, then recover and verify the second coordinate.03Algebra · Method guideSolving systems by eliminationAlign like terms, create opposite coefficients, add the equations, and recover the variable that was deliberately removed.04Algebra · Concept explainerOne solution, no solution, or infinitely many?For two linear equations, the coefficient pattern determines whether the graphs intersect once, never meet, or are actually the same line.05Algebra · Method guideCompound inequalities: and, or, and the sign flipSolve each condition, reverse the inequality only when multiplying or dividing by a negative, then combine by intersection or union.