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

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The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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

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

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If a number is divisible by 9, it is also divisible by which of the following?

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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