Topic Details (Notes format)

How to Solve Systems of Three Linear Equations

Subject: Mathematics

Book: Maths Mastery

Solving a system of three unknowns (x, y, z) typically uses substitution, elimination, or matrix methods like Gaussian elimination. For example, if you have x + y + z = 6, 2x – y + 3z = 8, and –x + 4y + 2z = 12, systematically combining equations can isolate one variable at a time. Alternatively, representing the system as a matrix and applying row operations speeds up the solution. These methods are crucial in engineering (analyzing networks), physics (forces in equilibrium), and advanced math modeling. Building skill in 3-variable systems extends your capacity to tackle multi-dimensional problems across disciplines.

Practice Questions

If x + y = 10 and xy = 21, what is the value of x³ + y³?

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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If x^2 + 4x + 4 = 0, what is the value of x?

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What is the sum of the first 20 odd numbers?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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The area of an equilateral triangle with side length 6 cm is:

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If x^2 - 6x + 9 = 0, what is the value of x?

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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