Mathematics Specification A - 4MA1 PearsonEdexcel

Simultaneous Linear Equations

Bayani Gaba-gaba

Some problems involve two unknowns connected by two conditions. A pair of simultaneous equations captures both conditions at once, and solving the system gives the unique values that satisfy both. This is one of the most useful algebraic techniques in the specification.

You will learn two methods for solving linear simultaneous equations: elimination and substitution. Higher-tier students also connect the algebra to the point where two straight lines cross on a graph.

Manufura

  1. Calculate the exact solution of two simultaneous equations in two unknowns
  2. [Higher] Interpret the equations as lines and the common solution as the point of intersection

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Takardar Darasi

If one apple and one banana cost 1.50, knowing just that is not enough to find the price of each fruit: an apple at 1.00 and a banana at 0.50 fit that clue just as well as an apple at 0.80 and a banana at 0.70. But if two apples and one banana cost 2.20, now you have two equations and can solve for both prices uniquely. That is the idea behind simultaneous equations.

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Nazarin Darasi

Barka da kammala darasi akan Simultaneous Linear Equations. Yanzu da kuka bincika mahimman ra'ayoyi da ra'ayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.

Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.

Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.

  1. Solve: x + y = 10 and x - y = 4. What is x? A) 3 B) 7 C) 6 D) 8 Answer: B
  2. Which method is best when one equation is y = 3x + 2? A) Trial and improvement B) Elimination C) Substitution D) Graphical Answer: C
  3. Solve: 2x + y = 8 and x + y = 5. What is y? A) 2 B) 3 C) 5 D) 1 Answer: A
  4. Two lines intersect at (3, 4). This means: A) The lines are parallel B) x = 3 and y = 4 satisfy both equations C) The gradient of both lines is 3 D) There is no solution Answer: B
  5. If 3a + 2b = 19 and a = 3, what is b? A) 3 B) 4 C) 5 D) 6 Answer: C

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Yi aikin wadannan tambayoyi a cikin manhaja

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