IGCSE Simultaneous Equations: Complete Guide for Cambridge IGCSE Mathematics

IGCSE simultaneous equations are essential algebra topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering solving by substitution and elimination method is essential for solving problems with multiple unknowns.

This comprehensive IGCSE simultaneous equations guide covers everything you need to know, including two methods for solving simultaneous equations, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to solve simultaneous equations using substitution and elimination methods, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Algebra practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Simultaneous Equations Matter

IGCSE simultaneous equations are essential algebra topics. Here’s why they’re so important:

• High frequency topic: Simultaneous equation questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for solving real-world problems with multiple variables
• Exam weight: Typically worth 5-8 marks per paper
• Real-world applications: Used in problem-solving across mathematics and science
• Problem-solving skills: Develops algebraic thinking and systematic problem-solving

Key insight from examiners: Students often struggle with choosing the right method or make arithmetic errors. This guide will help you master both methods systematically.

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Understanding Simultaneous Equations

Simultaneous equations are two or more equations with the same variables that are solved together.

Example:

• 2x + y = 7
• x - y = 2

We need to find values of x and y that satisfy both equations.

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Method 1: Substitution

Solve one equation for one variable, then substitute into the other equation.

Example 1: Solve:

• 2x + y = 7 … (1)
• x - y = 2 … (2)

Solution: From equation (2): x = y + 2 Substitute into (1): 2(y + 2) + y = 7 2y + 4 + y = 7 3y = 3 y = 1 Substitute back: x = 1 + 2 = 3

Answer: x = 3, y = 1

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Method 2: Elimination

Add or subtract equations to eliminate one variable.

Example 2: Solve:

• 3x + 2y = 11 … (1)
• x + 2y = 5 … (2)

Solution: Subtract (2) from (1): (3x + 2y) - (x + 2y) = 11 - 5 2x = 6 x = 3 Substitute into (2): 3 + 2y = 5 2y = 2 y = 1

Answer: x = 3, y = 1

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When Coefficients Don’t Match

Multiply one or both equations to make coefficients match.

Example 3: Solve:

• 2x + 3y = 13 … (1)
• 3x - y = 4 … (2)

Solution: Multiply (2) by 3: 9x - 3y = 12 … (3) Add (1) and (3): 11x = 25 x = 25/11 Substitute to find y.

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Step-by-Step Method

1. Choose method - Substitution or elimination
2. Manipulate equations - If needed, multiply to match coefficients
3. Eliminate variable - Solve for one variable
4. Substitute back - Find the other variable
5. Check - Verify both equations are satisfied

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Common Examiner Traps

• Arithmetic errors - Double-check calculations
• Wrong method choice - Substitution often easier when one variable is isolated
• Sign errors - Watch positive/negative signs carefully
• Forgetting to check - Always verify your answer

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Practice Questions

Question 1

Solve:

• x + y = 5
• 2x - y = 4

Solution: Add equations: 3x = 9, so x = 3 Substitute: 3 + y = 5, so y = 2

Answer: x = 3, y = 2

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Frequently Asked Questions About IGCSE Simultaneous Equations

What are simultaneous equations?

Simultaneous equations are two or more equations with the same variables that are solved together to find values that satisfy all equations.

What are the two methods for solving simultaneous equations?

1. Substitution - Solve one equation for one variable, substitute into the other
2. Elimination - Add or subtract equations to eliminate one variable

When should I use substitution?

Use substitution when one variable is easily isolated in one equation.

When should I use elimination?

Use elimination when coefficients are similar or can be made similar by multiplication.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Linear Equations: Complete Guide - Master linear equations
• IGCSE Quadratic Equations: Complete Guide - Master quadratic equations
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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