Learning to solve three simultaneous equations might seem daunting, but...
Further Maths176 views·Updated Jun 17, 2026·1 pageSolving Three Simultaneous Equations - AQA Further Maths Revision
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Solving Three Simultaneous Equations
Simultaneous equations with three unknowns require a strategic approach, but once you master the technique, you'll find it's quite straightforward. The key is systematically eliminating variables one by one.
Let's work through this example: x + y + z = 6 ①, 2x - y + z = 3 ②, and 3x + y - 2z = -1 ③. Start by adding equations to eliminate one variable - here we'll get rid of y first.
Adding equations ① and ② gives us 3x + 2z = 9 ④. Then adding equations ② and ③ gives us 5x - z = 2 ⑤. Notice how we now have two equations with just x and z!
To solve these remaining equations, multiply equation ⑤ by 2 to get 10x - 2z = 4 ⑥. Adding equations ④ and ⑥ eliminates z completely: 13x = 13, so x = 1. Substitute back to find z = 3, then use either original equation to find y = 2.
Top Tip: Always check your answer by substituting all three values back into each original equation - they should all balance perfectly!
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Further Maths176 views·Updated Jun 17, 2026·1 pageSolving Three Simultaneous Equations - AQA Further Maths Revision
Learning to solve three simultaneous equations might seem daunting, but it's actually a systematic process that builds on what you already know about solving pairs of equations. This mathematical skill is essential for A-level maths and opens doors to understanding...
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Solving Three Simultaneous Equations
Simultaneous equations with three unknowns require a strategic approach, but once you master the technique, you'll find it's quite straightforward. The key is systematically eliminating variables one by one.
Let's work through this example: x + y + z = 6 ①, 2x - y + z = 3 ②, and 3x + y - 2z = -1 ③. Start by adding equations to eliminate one variable - here we'll get rid of y first.
Adding equations ① and ② gives us 3x + 2z = 9 ④. Then adding equations ② and ③ gives us 5x - z = 2 ⑤. Notice how we now have two equations with just x and z!
To solve these remaining equations, multiply equation ⑤ by 2 to get 10x - 2z = 4 ⑥. Adding equations ④ and ⑥ eliminates z completely: 13x = 13, so x = 1. Substitute back to find z = 3, then use either original equation to find y = 2.
Top Tip: Always check your answer by substituting all three values back into each original equation - they should all balance perfectly!
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What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
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