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

What is the HCF of 72 and 120?

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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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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 value of x if log(x) + log(4) = log(32)?

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

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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What is the greatest common divisor (GCD) of 36 and 48?

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The probability of rolling a sum of 7 with two dice is:

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What is the sum of all even numbers between 1 and 50?

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

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