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# solve the system watch

1. 2y - x = sin x - sin 2y
cos x + 5 sin y = 4
2. Note that:

x + sin x = 2y + sin 2y. (1)

Clearly, x = 2y.

The question then becomes a simple case of substituting into equation (2) and solving a quadratic.

Hope this helps,

~~Simba
3. Beat me to it [by a long way ]

Just to show I have some degree of rigour [although this may be totally superfluous], to prove that x = 2y only, you can show that f(x) = sin(x) + x has a unique value; f(x) is 1-to-1.

f'(x) = cos(x) + 1
f'(x) >= 0

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Updated: July 19, 2008
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