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Mathematics · Grade 9

Systems of Equations and Inequalities

Learners solve pairs of linear equations by graphing, substitution and elimination, prove why elimination is valid, and classify systems by their number of solutions. They model ticket sales, mixtures and plan comparisons with systems, then graph linear inequalities and systems of inequalities to find and interpret feasible combinations under real constraints.

  • 4 lessons
  • About 125 minutes
  • Systems check: 11 questions
  • Ways to answer: fill in the blanks, choose an answer, draw a graph, plot points, type a number and put in order
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What learners will discover

  • Solve systems of two linear equations by graphing, substitution and elimination, and check solutions in both equations.
  • Explain why adding or scaling equations preserves the solutions of a system, and classify systems as having one, no or infinitely many solutions.
  • Model situations with systems of linear equations and interpret the solution in context.
  • Graph linear inequalities and systems of inequalities in two variables, and identify and interpret feasible points in context.

Lessons

  1. Solving by graphing and substitution 7 steps4 practiceabout 30 min
  2. Elimination and the number of solutions 7 steps4 practiceabout 32 min
  3. Modeling with systems 7 steps4 practiceabout 32 min
  4. Inequalities in two variables 7 steps5 practiceabout 31 min
  5. Systems check 11 questions at the end

Keep exploring

More 9th grade math

Guide for grown-ups