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Mathematics · Grade 8

Systems of Linear Equations

Learners see the solution of a system of two linear equations as the point that lies on both lines, check ordered pairs in both equations and solve systems by graphing. They use slopes and intercepts to recognise systems with no solution or infinitely many solutions, solve by substitution, elimination and inspection, and model real situations with systems whose solutions they interpret in context.

  • 4 lessons
  • About 95 minutes
  • Systems of linear equations check: 10 questions
  • Ways to answer: fill in the blanks, choose an answer, type a fraction, draw a graph, plot points and match pairs
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What learners will discover

  • Explain that a solution of a system of two linear equations is an ordered pair that makes both equations true (the intersection of the two graphs) and check whether a point solves a system.
  • Solve systems by graphing and use slopes and intercepts to recognise systems with no solution (parallel lines) or infinitely many solutions (the same line).
  • Solve systems algebraically by substitution, by elimination in simple cases and by inspection.
  • Write and solve systems of two linear equations for real-world and mathematical problems and interpret the solution in context.

Lessons

  1. What a solution of a system means 7 steps4 practiceabout 22 min
  2. Solving by graphing; parallel and identical lines 7 steps4 practiceabout 22 min
  3. Substitution and elimination 9 steps5 practiceabout 25 min
  4. Systems in context 8 steps5 practiceabout 26 min
  5. Systems of linear equations check 10 questions at the end

Keep exploring

Games to practice with

  • Number-Line HopHelp the frog hop to the right number — from counting to negative fractions.
  • Algebra BalanceKeep the scale level and the equation true, step by step.
  • Function FactoryFeed the machine, crack its rule and predict what comes out.

More 8th grade math

Guide for grown-ups