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 x + y = 10 and xy = 21, what is the value of x³ + y³?

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What is the value of x if 3x + 7 = 16?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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

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What is the probability of drawing an ace from a standard deck of 52 cards?

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A sphere has a radius of 7 cm. What is its volume?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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How many diagonals does a pentagon have?

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If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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