Free Grade 3 Simultaneous Equations Lesson Plans
Free Grade 3 lesson plans for Simultaneous Equations: 12 real questions with a full answer key and worked solutions. Simultaneous equations share the same solution. Eliminate or substitute one letter to find the other, then substitute back.
Free
Higher
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify simultaneous equations
Identify simultaneous equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain simultaneous equations
Explain simultaneous equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate simultaneous equations
Calculate simultaneous equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare simultaneous equations
Compare simultaneous equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Simultaneous Equations works
Simultaneous equations share the same solution. Eliminate or substitute one letter to find the other, then substitute back.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Solve: 1x + 4y = 20 and x − y = -5.[1]
- 2.Solve: 4x + 3y = 22 and x − y = 9.[1]
- 3.Solve: 1x + 2y = 21 and x − y = 0.[1]
- 4.Solve: 2x + 1y = 13 and x − y = 2.[1]
- 5.Solve: 3x + 2y = 7 and x − y = -1.[2]
- 6.Solve: 2x + 1y = -6 and x − y = 3.[2]
- 7.Solve: 3x + 1y = 17 and x − y = -5.[2]
- 8.Solve: 1x + 1y = 0 and x − y = 0.[2]
- 9.Solve: 4x + 2y = 4 and x − y = -8.[3]
- 10.Solve: 4x + 3y = -14 and x − y = 0.[3]
- 11.Solve: 2x + 4y = 44 and x − y = 1.[3]
- 12.Solve: 3x + 4y = 5 and x − y = 11.[3]
Show answers and working
1. x = 0, y = 5
From the second equation, x = y + -5. Substitute: 1(y + -5) + 4y = 20 → 5y = 25. y = 5, then x = 0.
2. x = 7, y = -2
From the second equation, x = y + 9. Substitute: 4(y + 9) + 3y = 22 → 7y = -14. y = -2, then x = 7.
3. x = 7, y = 7
From the second equation, x = y + 0. Substitute: 1(y + 0) + 2y = 21 → 3y = 21. y = 7, then x = 7.
4. x = 5, y = 3
From the second equation, x = y + 2. Substitute: 2(y + 2) + 1y = 13 → 3y = 9. y = 3, then x = 5.
5. x = 1, y = 2
From the second equation, x = y + -1. Substitute: 3(y + -1) + 2y = 7 → 5y = 10. y = 2, then x = 1.
6. x = -1, y = -4
From the second equation, x = y + 3. Substitute: 2(y + 3) + 1y = -6 → 3y = -12. y = -4, then x = -1.
7. x = 3, y = 8
From the second equation, x = y + -5. Substitute: 3(y + -5) + 1y = 17 → 4y = 32. y = 8, then x = 3.
8. x = 0, y = 0
From the second equation, x = y + 0. Substitute: 1(y + 0) + 1y = 0 → 2y = 0. y = 0, then x = 0.
9. x = -2, y = 6
From the second equation, x = y + -8. Substitute: 4(y + -8) + 2y = 4 → 6y = 36. y = 6, then x = -2.
10. x = -2, y = -2
From the second equation, x = y + 0. Substitute: 4(y + 0) + 3y = -14 → 7y = -14. y = -2, then x = -2.
11. x = 8, y = 7
From the second equation, x = y + 1. Substitute: 2(y + 1) + 4y = 44 → 6y = 42. y = 7, then x = 8.
12. x = 7, y = -4
From the second equation, x = y + 11. Substitute: 3(y + 11) + 4y = 5 → 7y = -28. y = -4, then x = 7.
Worked examples
Solve: 4x + 1y = 4 and x − y = 6.
- From the second equation, x = y + 6.
- Substitute: 4(y + 6) + 1y = 4 → 5y = -20.
- y = -4, then x = 2.
- Answer: x = 2, y = -4
Solve: 1x + 4y = 17 and x − y = -8.
- From the second equation, x = y + -8.
- Substitute: 1(y + -8) + 4y = 17 → 5y = 25.
- y = 5, then x = -3.
- Answer: x = -3, y = 5
Solve: 2x + 4y = 30 and x − y = -6.
- From the second equation, x = y + -6.
- Substitute: 2(y + -6) + 4y = 30 → 6y = 42.
- y = 7, then x = 1.
- Answer: x = 1, y = 7
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Stops after finding one letter.
Correction: Substitute back to find the second.
Subtracts equations with mismatched signs.
Correction: Same signs subtract, different signs add.
Teacher tips
- · Start with real-life pairs (2 coffees + 1 cake = …).
Parent tips
- · Puzzle: 2 apples and 1 banana cost $1.50…
Real-life applications
- · Working out two prices from two shopping bills.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Simultaneous Equations lesson plan really free?
- Yes. Every lesson plans on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Quadratics, Sequences, Number Sense. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Simultaneous Equations?
- Move on to Functions, Number Sense, Geometry, Measurement, which build directly on this idea.
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