Systems Summary

Algebra 1 · Axiom Academy

SUMMARY Systems of Linear Equations & Inequalities A review of the key methods for finding solutions that satisfy multiple conditions at once. A system is two or more equations or inequalities that share the same variables; a solution makes every one of them true at the same time. Geometrically, a solution is the point (or region) where the graphs of all the equations or inequalities meet. Three methods solve linear systems: graphing , substitution , and elimination — pick the one that fits the system's form. A linear system has exactly one of three outcomes: one solution , no solution , or infinitely many solutions . For systems of inequalities , the solution is the overlapping shaded region , not a single point. Core Concept Systems & Solutions A system bundles two or more equations (or inequalities) that share variables. A solution is a value for each variable that satisfies every statement in the system simultaneously. Geometric meaning: the point or region where all the graphs intersect. Check: substitute the candidate back into both equations. Core Concept Three Solving Methods Every linear system can be solved three ways — choose by the form of the equations. Graphing: plot both lines and read off the intersection. Best for seeing the concept. Substitution: isolate one variable, then sub its expression into the other equation. Ideal when a variable has coefficient 1 or -1 .

This is the written version of the interactive lesson above. See the full Algebra 1 course.