Topic Details (Notes format)

How to Solve Systems of Nonlinear Equations

Subject: Mathematics

Book: Maths Mastery

Systems where at least one equation is nonlinear (e.g., x² + y²=25 and x+y=7) require specialized approaches. You might solve for one variable, then substitute into the nonlinear equation, or use geometry (a line intersecting a circle) for interpretation. For instance, x+y=7 → y=7–x. Substituting into x²+(7–x)²=25 yields solutions for x. Nonlinear systems appear in conic section intersections, optimization problems, or advanced modeling tasks. Mastering them fosters a robust capacity to handle polynomial relationships and design solutions that go beyond straight lines.

Practice Questions

If a = 4 and b = 5, what is the value of (a+b)^2?

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

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

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

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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What is the cube of 4?

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