Free Grade 3 Elimination Method Lessons
Free Grade 3 lessons for Elimination Method: 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 elimination method
Identify elimination method accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain elimination method
Explain elimination method accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate elimination method
Calculate elimination method accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare elimination method
Compare elimination method 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 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: 2x + 2y = 6 and x − y = -1.[1]
- 2.Solve: 1x + 1y = 9 and x − y = 5.[1]
- 3.Solve: 2x + 3y = 4 and x − y = 12.[1]
- 4.Solve: 2x + 4y = -18 and x − y = 0.[1]
- 5.Solve: 2x + 4y = 22 and x − y = 5.[2]
- 6.Solve: 2x + 1y = 19 and x − y = -1.[2]
- 7.Solve: 1x + 4y = -10 and x − y = 0.[2]
- 8.Solve: 2x + 3y = 8 and x − y = -1.[2]
- 9.Solve: 2x + 2y = 8 and x − y = 10.[3]
- 10.Solve: 3x + 4y = 15 and x − y = 5.[3]
- 11.Solve: 3x + 1y = -4 and x − y = -8.[3]
- 12.Solve: 2x + 2y = -6 and x − y = 3.[3]
Show answers and working
1. x = 1, y = 2
From the second equation, x = y + -1. Substitute: 2(y + -1) + 2y = 6 → 4y = 8. y = 2, then x = 1.
2. x = 7, y = 2
From the second equation, x = y + 5. Substitute: 1(y + 5) + 1y = 9 → 2y = 4. y = 2, then x = 7.
3. x = 8, y = -4
From the second equation, x = y + 12. Substitute: 2(y + 12) + 3y = 4 → 5y = -20. y = -4, then x = 8.
4. x = -3, y = -3
From the second equation, x = y + 0. Substitute: 2(y + 0) + 4y = -18 → 6y = -18. y = -3, then x = -3.
5. x = 7, y = 2
From the second equation, x = y + 5. Substitute: 2(y + 5) + 4y = 22 → 6y = 12. y = 2, then x = 7.
6. x = 6, y = 7
From the second equation, x = y + -1. Substitute: 2(y + -1) + 1y = 19 → 3y = 21. y = 7, then x = 6.
7. x = -2, y = -2
From the second equation, x = y + 0. Substitute: 1(y + 0) + 4y = -10 → 5y = -10. y = -2, then x = -2.
8. x = 1, y = 2
From the second equation, x = y + -1. Substitute: 2(y + -1) + 3y = 8 → 5y = 10. y = 2, then x = 1.
9. x = 7, y = -3
From the second equation, x = y + 10. Substitute: 2(y + 10) + 2y = 8 → 4y = -12. y = -3, then x = 7.
10. x = 5, y = 0
From the second equation, x = y + 5. Substitute: 3(y + 5) + 4y = 15 → 7y = 0. y = 0, then x = 5.
11. x = -3, y = 5
From the second equation, x = y + -8. Substitute: 3(y + -8) + 1y = -4 → 4y = 20. y = 5, then x = -3.
12. x = 0, y = -3
From the second equation, x = y + 3. Substitute: 2(y + 3) + 2y = -6 → 4y = -12. y = -3, then x = 0.
Worked examples
Solve: 1x + 1y = 4 and x − y = 4.
- From the second equation, x = y + 4.
- Substitute: 1(y + 4) + 1y = 4 → 2y = 0.
- y = 0, then x = 4.
- Answer: x = 4, y = 0
Solve: 3x + 4y = -28 and x − y = 0.
- From the second equation, x = y + 0.
- Substitute: 3(y + 0) + 4y = -28 → 7y = -28.
- y = -4, then x = -4.
- Answer: x = -4, y = -4
Solve: 4x + 4y = 4 and x − y = -9.
- From the second equation, x = y + -9.
- Substitute: 4(y + -9) + 4y = 4 → 8y = 40.
- y = 5, then x = -4.
- Answer: x = -4, y = 5
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.
Every free resource for Elimination Method
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Elimination Method lesson really free?
- Yes. Every lessons 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. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Elimination Method?
- Move on to Substitution Method, Graphical Solutions, Algebraic Expressions, Equations, which build directly on this idea.
Related resources
Stuck on Elimination Method? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor