Simultaneous Equations
Understand that two linear equations can be solved simultaneously by finding the point where their graphs intersect, and interpret this graphically and algebraically as the pair of values satisfying both equations
Lesson
Set out your lesson
“Simultaneous Equations means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Two simple equation cards
- Pencil and scrap paper
Extra for the adult
Worked example. x+y=5 and x−y=1 → x=3, y=2 because 3+2=5 and 3−2=1.
Optional challenge. For Simultaneous Equations, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Simultaneous Equations, not mastery.
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Teaching approaches
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1 approach
Simultaneous Equations means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Two simple equation cards; Pencil and scrap paper. 1. Say the goal of Simultaneous Equations in plain words once. 2. Adult solves x+y=5 and x−y=1 by substitution or elimination. 3. Child solves three paired linear systems and checks each pair by substitution. 4. Fresh check: one fresh two-equation system. Record and stop. Done: three correct (x,y) pairs with a check. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Practice this concept
Start practiceSimultaneous Equations practice
Practice key ideas from Simultaneous Equations.
Free · no login · no ads · Practice answers and completion are not saved. Parent observation remains the lesson record.
Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
PhET Interactive Simulations · Practice link — not the full lesson
Graphing Lines
Before you open · source notes
Graphing Lines supports hands-on exploration for Simultaneous Equations. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Graphing Lines.” External page; Gakuva does not copy, host, embed, or redistribute materials.
Unknown — link only
Check understanding
- Explain that the intersection of two lines represents values satisfying both equations
- Find the approximate solution to a pair of simultaneous equations by reading a graph
- Verify a proposed solution by substituting into both equations
“Can your child explain that solving two equations simultaneously means finding the one pair of values that satisfies both at once — and show what that looks like on a graph?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 13–14
Standards