A worksheet on solving systems of equations (simultaneous equations) using the methods of substitution and elimination. There are 15 problems. Detailed solutions are included.

Equip your secondary mathematics students with this comprehensive, classroom-ready practice packet! Designed specifically for Key Stage 3, Foundation Tier GCSE, or Higher Tier GCSE students, this resource features a robust set of simultaneous linear equation questions complete with full, step-by-step worked solutions.

Whether you need a targeted homework task, an in-class practice workshop, a revision lesson before exams, or a dependable assessment, this packet provides a seamless way to build student confidence with algebraic methods, substitution, and elimination.
What is Included?

• Multi-Step Practice Questions: A wide variety of system structures that progress naturally from basic variable definitions to complex dual-coefficient equations.
• Full Step-by-Step Worked Solutions: Comprehensive algebraic breakdowns for every single simultaneous equation to save you hours of marking time and make grading a breeze.
• Dual Algebraic Methods: Comprehensive coverage that fits perfectly into any curriculum teaching both substitution and elimination methods.
• Versatile Layout: Cleanly organized layout with boxes that give students plenty of dedicated space to write out their working, equation numbers, and additions.

Core Concepts Covered

• Solving linear systems using substitution by plugging isolated variable terms directly into secondary equations.
• Applying the elimination method by adding or subtracting balanced linear equations to cancel out a variable.
• Multiplying equations by a constant value to create matching coefficients for elimination.
• Rearranging algebraic expressions before applying calculation steps.
• Handling positive integers, negative coefficients, and fractional fractions smoothly.

Perfect For:

• Daily Homework or Independent Learning Tasks
• Small-Group Intervention & Maths Remediation
• End of Topic Assessment & Exam RevisionQuick and Easy Emergency Cover Plans

Curriculum Alignment

• Key Stage 3 Mathematics: Covers algebraic proficiency, model relationships, and moving towards solving simultaneous linear equations.
• GCSE Mathematics (Foundation & Higher): Directly targets solving quadratic or linear simultaneous equations algebraically, finding exact solution intersections, and manipulating algebraic terms.