Question

how to do this sum?​

Answer 1

Answer:

x = a, y = b

Step-by-step explanation:

Given :

1st equation: ${\sf{\ \ {\dfrac{x}{a}} = {\dfrac{y}{b}} }}$

• Transposing the term.

$\implies{\sf{ {\dfrac{x}{a}} - {\dfrac{y}{b}} = 0}}$

• On further solving, we get

$\implies{\sf{ {\dfrac{x(b) - y(a)}{ab}}}}$

$\implies{\sf{ {\dfrac{bx - ay}{ab}} = 0}}$

$\implies$ bx - ay = 0

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2nd equation: ax + by = a² + b²

Now,

• Multiplying the 1st equation by a and 2nd equation by b, we get

→ a(bx - ay) = a(0)

→ b(ax + by) = b(a² + b²)

• On further solving, we get

→ abx - a²y = 0 __________(1)

→ abx + b²y = b(a² + b²) _________(2)

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• Subtracting (1) and (2).

→ (abx - a²y) - (abx + b²y) = (0) - [ b(a² + b²) ]

→ abx - a²y - abx - b²y = - b(a² + b²)

→ - a²y - b²y = - b(a² + b²)

• Taking common terms out.

→ - y(a² + b²) = - b(a² + b²)

• Cancelling the common term.

→ y = b

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Substituting this in 1st equation.

→ bx - a(b) = 0

→ bx - ab = 0

→ bx = ab

→ x = ${\sf{\ {\dfrac{ab}{b}}}}$

→ x = a