Topic Details (Notes format)

How to Solve Linear Equations (Two Variables)

Subject: Mathematics

Book: Maths Mastery

Systems of linear equations with two variables commonly follow the format: ax + by = c and dx + ey = f. You can solve these using substitution, elimination, or graphical interpretation. For instance, consider the system x + y = 5 and x – y = 1. Adding the two equations gives 2x = 6, so x = 3. Substituting x = 3 back into x + y = 5 yields y = 2. Systems of linear equations model various scenarios—calculating the intersection of supply and demand curves, planning mixture problems, or analyzing motion. A solid understanding of these solutions is essential for real-world planning and higher-level math endeavors.

Practice Questions

If the perimeter of a square is 40 cm, what is the area of the square?

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If the sum of three consecutive integers is 96, what are the integers?

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If a square has a perimeter of 64 cm, what is its area?

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What is the area of an equilateral triangle with side length 10 cm?

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If the sum of the angles of a polygon is 1080°, how many sides does the polygon have?

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How many ways can 4 people sit in a row?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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If the average of five consecutive odd numbers is 25, what is the largest number?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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What is the value of log₃(27)?

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