Topic Details (Notes format)

How to Solve Systems of Inequalities

Subject: Mathematics

Book: Maths Mastery

Systems of inequalities involve multiple constraints that define a region of acceptable solutions on a coordinate plane. Consider x + y ≤ 5 and x – y ≥ –1. Graph these lines (x + y = 5 and x – y = –1), then shade the areas that satisfy each inequality. The solution set is where shaded regions overlap. Systems of inequalities appear in linear optimization, resource management, and real-world planning problems like deciding feasible production levels within time and budget constraints. Mastering this visualization and computation process enables you to handle a broad range of practical optimization tasks.

Practice Questions

If 5x - 2 = 13, what is the value of x?

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

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A cube has a side length of 4 cm. What is its volume?

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What is the sum of the first 50 positive integers?

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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A car travels 240 km in 4 hours. What is its average speed?

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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