The number of all possible ordered pairs `(x, y), x, y in R` satisfying the system of equations `x + y = (2pi)/(3), cos x + cos y = (3)/(2)` is

Answer

0

Explanation

We have `cos x + cos y = (3)/(2)`
`rArr 2 cos ((x + y)/(2)) cos ((x - y)/(2)) = (3)/(2)`
`rArr 2 cos '(pi)/(3) cos ((x - y)/(2)) = (3)/(2)`
[using `x + y = (2pi)/(3)`]
`rArr cos ((x - y)/(2)) = (3)/(2)`, which is not possible
Hence, the system of equlibrium has not solution.