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

View Question

The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

View Question

If the product of two numbers is 120 and their sum is 26, what are the numbers?

View Question

The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

View Question

What is the sum of all odd numbers from 1 to 99?

View Question

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

View Question

What is the probability of drawing a king from a standard deck of 52 playing cards?

View Question

If x - y = 5 and x + y = 15, what is the value of x?

View Question

What is the LCM of 15 and 20?

View Question

The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

View Question