Study Guide
Simultaneous Equations: Substitution and Elimination
Shows Year 10 students how to solve a pair of linear equations by substitution and by elimination, including when to multiply an equation…
- Difficulty
- Level 2 · Standard
- Time
- 20 min
WorksheetYear 10Level 3 · Challenge
Free Year 10 Simultaneous Equations Worksheet — Level 3
Solve pairs of linear equations by elimination or substitution. A challenge set for students ready to stretch further. This Year 10 worksheet has 8 questions and comes with a full answer sheet showing the working for every question.
Instant download · No sign-up · Free for personal, classroom and homeschool use
- Year
- Year 10
- Subject
- Mathematics
- Topic
- Simultaneous Equations
- Difficulty
- Level 3 · Challenge
- Estimated time
- 20 minutes
- Curriculum
- Australian Curriculum
- Questions
- 8
- Answers
- Included, with working
- Format
- PDF (A4) + print
Students will practise
- solving simultaneous equations by elimination
- substituting to find the second variable
- checking solutions
Curriculum: Australian Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.
What's next?
Completed: Year 10 Simultaneous Equations Worksheet — Level 3
Ready for more? Move on to Year 11 Mathematics.
How to use this worksheet
- Print the PDF or complete it on screen. Write the student's name and date at the top.
- Read the instructions for each part together before starting. Encourage working to be shown, not just answers.
- Mark with the answer sheet. Compare the method, not only the final answer, and give credit for correct working.
- Record the score, celebrate what went well, then follow the "What's next" suggestion.
Common questions
Who is this worksheet for?
Year 10 students (typically ages 15–16) working on simultaneous equations. It is pitched at level 3 · challenge; an easier version is linked above.
Are the answers included?
Yes. The PDF includes a full answer sheet with the working for every question. You can also view the answers online.
How long does it take?
About 20 minutes for 8 questions. Short, regular sessions work best: two or three a week beats one long one.
Do I need to sign up to download?
No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.
What should we do next?
Explore more Year 10 mathematics resources.
Preview
Year 10 · Mathematics · Simultaneous Equations
Year 10 Simultaneous Equations Worksheet — Level 3
Success Tutoring
Student name:
Date:
Score: /
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 3x + 3y = 6 and 2x − 5y = −17
2.Solve simultaneously: 4x + 2y = 28 and 2x + 2y = 18
3.Solve simultaneously: 3x − y = −3 and 3x + 3y = −15
4.Solve simultaneously: 3x − 4y = −6 and 4x − 5y = −6
5.Solve simultaneously: 2x + 3y = 27 and 2x − 3y = −3
6.Solve simultaneously: 3x − 3y = −39 and 3x + 2y = −4
7.Solve simultaneously: 3x + y = 21 and 4x − 5y = 47
8.Solve simultaneously: 2x − y = 1 and 2x + 4y = 36
Preview — the PDF contains the full resource and answer sheet.
More Year 10 simultaneous equations resources
- Worksheet
Year 10 Simultaneous Equations Worksheet — Level 2
Solve pairs of linear equations by elimination or substitution. Expected-level practice for this year group. This Year 10 worksheet has 8…
- Difficulty
- Level 2 · Standard
- Time
- 20 min
- Questions
- 8 questions
- Answers
- Answers included
Simultaneous Equations in other year levels
- Year 9 Simultaneous Equations Worksheet — Level 1
Worksheet · Year 9 · Simultaneous Equations · Level 1 · Easier
- Year 11 Simultaneous Equations Worksheet — Level 3
Worksheet · Year 11 · Simultaneous Equations · Level 3 · Challenge
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About this resource
- Created by
- Success Tutoring Maths Team
- Reviewed by
- Success Tutoring
- Last reviewed
- 1 October 2026
- How it was made
- Generated by checked procedures
Free to print and share for personal, classroom and homeschool use. Please don't resell. Spotted an error? Let us know.