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Let [a] denotes the larger integer not e...

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]`

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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.
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Knowledge Check

  • If x and y satisfy te equation xy-2x^(2)-9x+3y-16=0 then

    A
    number of ordered pair `(x,y)` is 4 where `x,y in Z`
    B
    number of ordered paire `(x,y)` is 1 where `x,y in N`
    C
    if `xge y, x, y in N` then number of ordered pair is zero
    D
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  • If x and y satisfy the equation y = 2[x]+9 and y = 3[x+2] simultaneously, the [x+y] is (where [x] is the greatest integer function)

    A
    `21`
    B
    `18`
    C
    `30`
    D
    `12`

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