Topic Details (Notes format)

How to Graph Linear Inequalities in Two Variables

Subject: Mathematics

Book: Maths Mastery

For a two-variable inequality such as y<2x+3, first graph the line y=2x+3. Because the inequality is strict (<), draw a dashed line. Then pick a test point not on the line (often (0,0)) to see which side satisfies the inequality. Shade that region. If y≤2x+3, use a solid line. This technique extends to design problems, feasible regions in linear programming, or any scenario bounding solutions in 2D. Consistent application ensures clarity on possible (x,y) pairs within real-world constraints like supply-demand, cost/time tradeoffs, or geometric regions.

Practice Questions

If a:b = 3:4 and b:c = 5:6, what is a:c?

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If two complementary angles differ by 30°, what are the angles?

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

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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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A number is increased by 20% and then decreased by 10%. What is the net change?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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If 8x = 512, what is the value of x?

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A number is increased by 20% and then decreased by 20%. What is the net change?

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What is the square root of 0.25?

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