MathematicsIf ax+y=by+z=cz-x, then which of the following equations is true?

If ax+y=by+z=cz-x, then which of the following equations is true?


  1. A
    a=b+c
  2. B
    c=a+b
  3. C
    b=a × c
  4. D
    b=a+c  

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    Solution:

    Given equation is ax+y=by+z=cz-x.
    Let ax+y=by+z=cz-x=k .
    ⇒ a=xk+yk … (1)
    ⇒ b=yk+zk … (2)
    ⇒ c=zk-xk … (3)
    Adding (1), (3) gives,
    ⇒ a+c=zk-xk+xk+yk ⇒ a+c=zk+yk … (from 2).
     ∴ a+c=b Hence, the correct option is 4.
     
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