Systems of Equations
Solving systems by graphing, substitution, and elimination.
This page is a free outline of what the Systems of Equations lesson covers — it is not the lesson itself. The interactive lesson, practice, quizzes, and AI Tutor are inside the app.
This lesson covers
- Elimination Method (Systems) Elimination solves a system by adding or subtracting the two equations so one variable cancels — multiplying an equation first, if needed, to line up opposite coefficients.
- Solving Systems by Graphing Graphing solves a system by drawing both lines: the point where they cross is the (x, y) solution that satisfies both equations.
- Substitution Method (Systems) Substitution solves a system by isolating one variable in one equation and plugging that expression into the other, reducing it to a single-variable equation.
- Systems of Equations – Identifying & Solutions A system of equations is two equations with two unknowns; its solution is the single (x, y) pair that makes both true at once.
- Systems of Equations – Special Cases (No / Infinite Solutions) A system has no solution when its lines are parallel (never cross), and infinitely many when the two equations are really the same line.
- Two-Variable Word Problems A word problem with two unknowns, captured as equations in x and y (often a system) instead of a single-variable equation.
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Inside the app, Systems of Equations comes with:
Read the explanation here for free — then practice it for real, with everything you need in one place.
24/7 AI Tutor — Ask anything and get a step-by-step explanation when you’re stuck — it teaches the concept, not just the answer. Every answer verified by three independent AIs.
- Practice sets — Open-book practice questions at your level, easiest-first — as many as you want, never scored.
- Quizzes — Scored quizzes on the whole lesson, so you know when you’re ready to move on.
- Skills Check — A concept-by-concept map of what you’ve mastered and what to focus on next.
- Worked examples — Tap the Brain Button on any example for alternative step-by-step explanations.
- Glossary — Plain-English definitions of every key term in the lesson.
- Formula sheet — The GED® & HiSET® formula sheets, on screen while you practice.
- Practice calculator — An on-screen calculator to build your calculator skills before test day.
- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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