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Question

Solve for x and y

ax + by = 2ab

bx + ay = a​​​​​​2 + b​​​​​​2

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Solution

ax + by + bx +ay = a² + 2ab + b²

rearrange the left side.

ax + ay + bx + by = a² + 2ab + b²

a(x+y) + b(x +y) = a²+ 2ab + b²
(a+b)(x+y) = a² + 2ab + b²
(a+b)(x+y) = (a+b)²
x + y = a+b

x = a+ b - y
y = a + b - x

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