Mathematics - Additional - 0606 CIE

Simultaneous Equations

Muhtasari

Solving two linear equations together is familiar ground. Now one of the equations becomes non-linear, perhaps a curve such as a circle or a parabola. Geometrically you are finding where a straight line meets a curve, and there can be two crossing points, one (a tangent) or none.

In this lesson you will learn the reliable substitution method: rearrange the linear equation, substitute it into the non-linear one, and solve the quadratic that results. The classic example, a line meeting a circle, shows the whole process and connects neatly to coordinate geometry.

Malengo

Solve simultaneous equations in two unknowns by elimination or substitution, including cases with one linear and one non-linear equation.

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Maelezo ya Somo

Whenever a straight-line relationship meets a curved one, you are solving a linear and a non-linear equation together: a supply line crossing a demand curve, a path meeting a boundary, a sightline touching a circle. The substitution method here is the workhorse for all such problems and feeds directly into the circle-and-line topics later in the course.

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Tathmini ya Somo

Hongera kwa kukamilisha somo la Simultaneous Equations. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.

Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.

Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.

Solving y = x + 1 and x^2 + y^2 = 25 leads to which quadratic in x? A. x^2 + x - 12 = 0 B. x^2 - x - 12 = 0 C. 2x^2 + 25 = 0 D. x^2 + 1 = 25 Answer: A
The points of intersection of y = x + 1 and x^2 + y^2 = 25 are: A. (4, 5) and (-3, -2) B. (-4, -3) and (3, 4) C. (0, 1) and (5, 6) D. (3, -4) and (-4, 3) Answer: B
To solve one linear and one non-linear equation, the best first step is to: A. Add the two equations B. Square the linear equation C. Substitute the linear equation into the non-linear one D. Multiply the equations Answer: C
Solving y = 2x - 1 and y = x^2 - 4 gives the x-values: A. 3 and -1 B. 1 and -3 C. 2 and -2 D. 4 and -1 Answer: A
If a line meets a curve at exactly one point, the line is: A. A chord B. A tangent C. Parallel to an axis D. Outside the curve Answer: B

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Vitabu Vinavyopendekezwa

Cambridge IGCSE Mathematics Core and Extended Coursebook

Manukuu: Second edition

Mchapishaji: Cambridge University Press

Mwaka: 2018

ISBN: 978-1-108-43718-9

Maelezo: Endorsed coursebook with full coverage of the 0580/0980 syllabus, worked examples and practice exercises.

Cambridge IGCSE Core and Extended Mathematics

Manukuu: Fifth edition

Mchapishaji: Hodder Education

Mwaka: 2023

ISBN: 978-1-398-37391-4

Maelezo: Endorsed textbook with worked examples and graded questions across Core and Extended content.

Jifunze zaidi kutoka vyanzo huria

Sehemu ya kitabu Systems of Nonlinear Equations and Inequalities: Two Variables OpenStax · Algebra and Trigonometry
Solve a system of nonlinear equations using substitution.

"Algebra and Trigonometry: Systems of Nonlinear Equations and Inequalities: Two Variables" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/11-3-systems-of-nonlinear-equations-and-inequalities-two-variables. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction

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