Algebra course topic

Systems & Inequalities

Solve simultaneous conditions, choose an efficient method, and describe whole solution regions instead of isolated numbers.

Understand the idea

Direct answers and concept explanations that make the structure visible.

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.Algebra IConcept explainer

Work the method

Repeatable procedures with worked examples and checks.

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.Algebra IMethod guide 03Algebra · Method guideSolving systems by eliminationAlign like terms, create opposite coefficients, add the equations, and recover the variable that was deliberately removed.Algebra IMethod guide 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.Algebra IMethod guide 06Algebra · Method guideGraphing linear inequalities in two variablesDraw the boundary, decide whether it belongs to the solution, then test a point to choose the correct half-plane.Algebra IMethod guide

Choose a strategy

Comparisons for the moments when several methods look possible.

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.Algebra IDecision guide