Free Grade 3 Elimination Method in Context Common Errors Lessons
Free Grade 3 lessons for Elimination Method in Context 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
Foundation
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify elimination method in context common errors
Identify elimination method in context common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain elimination method in context common errors
Explain elimination method in context common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate elimination method in context common errors
Calculate elimination method in context common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare elimination method in context common errors
Compare elimination method in context 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 Elimination Method in Context 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: 4x + 4y = -28 and x − y = 1.[1]
- 2.Solve: 4x + 3y = 6 and x − y = -2.[1]
- 3.Solve: 2x + 3y = 22 and x − y = 1.[1]
- 4.Solve: 3x + 2y = 20 and x − y = 10.[1]
- 5.Solve: 1x + 2y = -1 and x − y = 2.[2]
- 6.Solve: 3x + 1y = 17 and x − y = 7.[2]
- 7.Solve: 3x + 2y = -1 and x − y = 3.[2]
- 8.Solve: 1x + 2y = 10 and x − y = 7.[2]
- 9.Solve: 4x + 3y = -3 and x − y = -6.[3]
- 10.Solve: 1x + 4y = 0 and x − y = 10.[3]
- 11.Solve: 3x + 4y = 6 and x − y = -5.[3]
- 12.Solve: 1x + 2y = 8 and x − y = 2.[3]
Show answers and working
1. x = -3, y = -4
From the second equation, x = y + 1. Substitute: 4(y + 1) + 4y = -28 → 8y = -32. y = -4, then x = -3.
2. x = 0, y = 2
From the second equation, x = y + -2. Substitute: 4(y + -2) + 3y = 6 → 7y = 14. y = 2, then x = 0.
3. x = 5, y = 4
From the second equation, x = y + 1. Substitute: 2(y + 1) + 3y = 22 → 5y = 20. y = 4, then x = 5.
4. x = 8, y = -2
From the second equation, x = y + 10. Substitute: 3(y + 10) + 2y = 20 → 5y = -10. y = -2, then x = 8.
5. x = 1, y = -1
From the second equation, x = y + 2. Substitute: 1(y + 2) + 2y = -1 → 3y = -3. y = -1, then x = 1.
6. x = 6, y = -1
From the second equation, x = y + 7. Substitute: 3(y + 7) + 1y = 17 → 4y = -4. y = -1, then x = 6.
7. x = 1, y = -2
From the second equation, x = y + 3. Substitute: 3(y + 3) + 2y = -1 → 5y = -10. y = -2, then x = 1.
8. x = 8, y = 1
From the second equation, x = y + 7. Substitute: 1(y + 7) + 2y = 10 → 3y = 3. y = 1, then x = 8.
9. x = -3, y = 3
From the second equation, x = y + -6. Substitute: 4(y + -6) + 3y = -3 → 7y = 21. y = 3, then x = -3.
10. x = 8, y = -2
From the second equation, x = y + 10. Substitute: 1(y + 10) + 4y = 0 → 5y = -10. y = -2, then x = 8.
11. x = -2, y = 3
From the second equation, x = y + -5. Substitute: 3(y + -5) + 4y = 6 → 7y = 21. y = 3, then x = -2.
12. x = 4, y = 2
From the second equation, x = y + 2. Substitute: 1(y + 2) + 2y = 8 → 3y = 6. y = 2, then x = 4.
Worked examples
Solve: 1x + 1y = 13 and x − y = 3.
- From the second equation, x = y + 3.
- Substitute: 1(y + 3) + 1y = 13 → 2y = 10.
- y = 5, then x = 8.
- Answer: x = 8, y = 5
Solve: 2x + 3y = -5 and x − y = -5.
- From the second equation, x = y + -5.
- Substitute: 2(y + -5) + 3y = -5 → 5y = 5.
- y = 1, then x = -4.
- Answer: x = -4, y = 1
Solve: 1x + 3y = 14 and x − y = -10.
- From the second equation, x = y + -10.
- Substitute: 1(y + -10) + 3y = 14 → 4y = 24.
- y = 6, then x = -4.
- Answer: x = -4, y = 6
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
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- Start with Elimination Method in Context Word Problems, Elimination Method in Context Techniques, Working with Elimination Method. Each one has its own free lesson, worksheet and quiz.
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- Move on to Introducing Elimination Method, Working with Elimination Method, which build directly on this idea.
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