Free Grade 3 Introducing Elimination Method Common Errors Lesson Plans
Free Grade 3 lesson plans for Introducing Elimination Method Common Errors: 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing elimination method common errors
Identify introducing elimination method common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing elimination method common errors
Explain introducing elimination method common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing elimination method common errors
Calculate introducing elimination method common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing elimination method common errors
Compare introducing elimination method common errors 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 Introducing Elimination Method Common Errors 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 + 2y = 9 and x − y = 0.[1]
- 2.Solve: 3x + 4y = 8 and x − y = 12.[1]
- 3.Solve: 1x + 2y = 3 and x − y = -3.[1]
- 4.Solve: 4x + 2y = -20 and x − y = 1.[1]
- 5.Solve: 3x + 1y = 27 and x − y = 5.[2]
- 6.Solve: 4x + 4y = 44 and x − y = -5.[2]
- 7.Solve: 2x + 4y = 18 and x − y = 6.[2]
- 8.Solve: 1x + 4y = 0 and x − y = 0.[2]
- 9.Solve: 2x + 4y = 24 and x − y = -6.[3]
- 10.Solve: 1x + 4y = 4 and x − y = -6.[3]
- 11.Solve: 2x + 1y = -6 and x − y = -6.[3]
- 12.Solve: 3x + 1y = 5 and x − y = -5.[3]
Show answers and working
1. x = 3, y = 3
From the second equation, x = y + 0. Substitute: 1(y + 0) + 2y = 9 → 3y = 9. y = 3, then x = 3.
2. x = 8, y = -4
From the second equation, x = y + 12. Substitute: 3(y + 12) + 4y = 8 → 7y = -28. y = -4, then x = 8.
3. x = -1, y = 2
From the second equation, x = y + -3. Substitute: 1(y + -3) + 2y = 3 → 3y = 6. y = 2, then x = -1.
4. x = -3, y = -4
From the second equation, x = y + 1. Substitute: 4(y + 1) + 2y = -20 → 6y = -24. y = -4, then x = -3.
5. x = 8, y = 3
From the second equation, x = y + 5. Substitute: 3(y + 5) + 1y = 27 → 4y = 12. y = 3, then x = 8.
6. x = 3, y = 8
From the second equation, x = y + -5. Substitute: 4(y + -5) + 4y = 44 → 8y = 64. y = 8, then x = 3.
7. x = 7, y = 1
From the second equation, x = y + 6. Substitute: 2(y + 6) + 4y = 18 → 6y = 6. y = 1, then x = 7.
8. x = 0, y = 0
From the second equation, x = y + 0. Substitute: 1(y + 0) + 4y = 0 → 5y = 0. y = 0, then x = 0.
9. x = 0, y = 6
From the second equation, x = y + -6. Substitute: 2(y + -6) + 4y = 24 → 6y = 36. y = 6, then x = 0.
10. x = -4, y = 2
From the second equation, x = y + -6. Substitute: 1(y + -6) + 4y = 4 → 5y = 10. y = 2, then x = -4.
11. x = -4, y = 2
From the second equation, x = y + -6. Substitute: 2(y + -6) + 1y = -6 → 3y = 6. y = 2, then x = -4.
12. x = 0, y = 5
From the second equation, x = y + -5. Substitute: 3(y + -5) + 1y = 5 → 4y = 20. y = 5, then x = 0.
Worked examples
Solve: 2x + 4y = 28 and x − y = 2.
- From the second equation, x = y + 2.
- Substitute: 2(y + 2) + 4y = 28 → 6y = 24.
- y = 4, then x = 6.
- Answer: x = 6, y = 4
Solve: 2x + 1y = -9 and x − y = -3.
- From the second equation, x = y + -3.
- Substitute: 2(y + -3) + 1y = -9 → 3y = -3.
- y = -1, then x = -4.
- Answer: x = -4, y = -1
Solve: 2x + 2y = 20 and x − y = -6.
- From the second equation, x = y + -6.
- Substitute: 2(y + -6) + 2y = 20 → 4y = 32.
- y = 8, then x = 2.
- Answer: x = 2, y = 8
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
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- What should a learner already know before this?
- Start with Introducing Elimination Method Word Problems, Introducing Elimination Method Techniques, Quadratics. Each one has its own free lesson, worksheet and quiz.
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- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Introducing Elimination Method Common Errors?
- Move on to Working with Elimination Method, Elimination Method in Context, which build directly on this idea.
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