Question

A-Множество решений уравнения 4x+5y=c. B-множество решений уравнения 3x+4y=k.Найдите x+y

Answer 1

1.4 x + 5 y = c

Geometric figure:

Properties

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Alternate forms:

y = c/5 - (4 x)/5

-c + 4 x + 5 y = 0

Real solution:

y = c/5 - (4 x)/5

Solution:

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y = c/5 - (4 x)/5

Integer solution:

x = 4 c + 5 n,   y = -3 c - 4 n,   n element Z

Solution for the variable y:

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y = 1/5 (c - 4 x)

Derivative:

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d/dx(4 x + 5 y) = 4

Implicit derivatives:

More

(dx(y, c))/(dc) = 1/4

(dx(y, c))/(dy) = -5/4

(dy(x, c))/(dc) = 1/5

(dy(x, c))/(dx) = -4/5

(dc(x, y))/(dy) = 5

(dc(x, y))/(dx) = 4

2.3 x + 4 y = k

Geometric figure:

Properties

line

Alternate forms:

y = k/4 - (3 x)/4

-k + 3 x + 4 y = 0

Real solution:

y = k/4 - (3 x)/4

Solution:

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y = k/4 - (3 x)/4

Integer solution:

x = 3 k + 4 n,   y = -2 k - 3 n,   n element Z

Solution for the variable y:

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y = 1/4 (k - 3 x)

Derivative:

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d/dx(3 x + 4 y) = 3

Implicit derivatives:

More

(dx(y, k))/(dk) = 1/3

(dx(y, k))/(dy) = -4/3

(dy(x, k))/(dk) = 1/4

(dy(x, k))/(dx) = -3/4

(dk(x, y))/(dy) = 4

(dk(x, y))/(dx) = 3