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

A number is increased by 20% and then decreased by 20%. What is the net change?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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What is the sum of all angles in a hexagon?

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What is the area of a circle with a diameter of 14 cm?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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If 5x - 2 = 13, what is the value of x?

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What is the LCM of 15 and 20?

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If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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