Number of solutions to system of equations sin frac{x+y}{2}=0 and |x| + |y| = 1

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Trigonometrical Equations

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Number of solutions to the system of equations $sin \frac{x+y}{2}=0$ and $|x| + |y| = 1$

A

$2$

B

$3$

C

$4$

D

$6$

Solution

$\because \sin \left(\frac{\mathrm{x}+\mathrm{y}}{2}\right)=0 \Rightarrow \mathrm{x}+\mathrm{y}=2 \mathrm{n} \pi$

$ and\,\,\,\, |x|+|y|=1$.

By graph, only $2$ solutions.

Standard 11

Mathematics

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