Let `[a]` denotes the larger integer not exceeding the real number `a` if `x` and `y` satisfy the equations `y=2[x]+3` and `y=3[x-2[` simultaneously determine `[x+y]`

Explanation

We have `y=2[x]+3=3[x-2]`……i ltbr `implies2[x]+3=3([x]-2)`[from property (i)]
`implies2[x]+3=3[x]-6`
`implies[x]=9`
From Eq. (i) `y=2xx9+3=21`
`:.[x+y]=[x+21]=[x]+21=9+21=30`
hence the value of `[x+y]` is 30.