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 cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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What is the remainder when 5^100 is divided by 3?

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The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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What is the LCM of 15 and 20?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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What is the sum of all angles in a hexagon?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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What is the sum of the first 20 odd numbers?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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