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

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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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If the length of a rectangle is doubled and the width is halved, what is the change in area?

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

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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What is the sum of the first 20 odd numbers?

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What is the probability of drawing a king from a standard deck of 52 playing cards?

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A triangle has angles 60°, 60°, and 60°. What type of triangle is it?

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