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Solving Systems of Inequalities

Mathematics Grade 8 Difficulty 2/5

Beginning of the lesson

Solving Systems of Inequalities

Big Idea: A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all ordered pairs $(x, y)$ that satisfy every inequality in the system simultaneously.

📌 What Is a System of Inequalities?

You already know how to solve a single linear inequality like $y > 2x + 1$. Its solution is an entire half-plane — a shaded region on one side of the boundary line.

A system of inequalities combines two or more such inequalities. For example:

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  • Worked examples
  • Common mistakes and how to avoid them
  • Test questions: 105
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