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Patterns within systems of linear equations

This task will have you investigate linear equations in which the constants have a well-known

mathematical pattern.


Consider the following, linear equations whose constants follow a well-known pattern:

x+2y =4

25x+5y = 1

3x+y = 1/3

2x-6y = 18

• Examine the constants within each individual equation and describe the well-known pattern

common to the constants in each equation.

• Give several other examples of equations fitting this pattern. Rewrite these equations in the form y = mx + b.

• Write the general equations for this pattern of constants in both standard (Ax + By = C) form and slope-intercept (y = mx + b) form. How are the constants A, B, C, m, and b related to each other? Explain why this is so.

Репетитор по IB Maths - Математика для International Baccalaureates

IB Math Exam, A-level, SAT помощь по Skype

Курсовые, Контрольные, Экзамены

Решение задач и контрольных работ на заказ. Математика. Решение контрольных работ.

Now consider the entire family of linear equations fitting this pattern.

• On the same set of axes, graph a large sampling of representatives of this family, being sure to include a wide range of slopes. You may wish to explore this family further using the dynamic/ animated display features of your calculator or graphing software. Describe the graphical pattern you observe.

Patterns within systems of linear equations


the coefficients follow a geometric progression

the constants exhibit the same well known patterns

x + qy = q2

for two linear equations whose coefficients follow a geometric progression with ratios r and s,

the point of intersection is (- rs, r + s)

It is a conjecture to be proved.

the points of intersection are always (-1, 2)
Hence we can conclude that for any 2x2 system of linear equations whose coefficients follow an arithmetic progression,
the values of x and y will always be -1 and 2 respectively.

Рубрика "нам пишут и просят помочь на экзамене по математике и физике"

Я собрался поступать в ЗФТШ, и мне будет нужна помощь в решении заданий, в которых я не справлюсь.
Вступительные будут по физике и математике.
Давайте обсудим цену и способ обмена информацией на вступительной контрольной работе в ВФТШ при МФТИ.

Отзыв о репетиторе МФТИ Алексее Эдуардовиче Султанове



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