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

What is the LCM of 15 and 20?

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

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What is the sum of all angles in a hexagon?

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

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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