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 x² - 9x + 18 = 0, what are the roots of the equation?

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

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What is the square root of 0.25?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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

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If the sum of three consecutive integers is 72, what are the integers?

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What is the cube root of 729?

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What is the sum of the interior angles of a hexagon?

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What is the length of the diagonal of a square with a side length of 7 cm?

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What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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