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 + 1/x = 5, what is the value of x^2 + 1/x^2?

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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What is the value of log₃(27)?

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

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If a number is divisible by 9, it is also divisible by which of the following?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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