MathematicsSolve for x and y x a + y b =2 ax−by = a 2 − b 2  

Solve for x and y


x a + y b =2 axby = a 2 b 2  


  1. A
    x = a and y = b
  2. B
    x = -a and y = b
  3. C
    x = a and y = -b
  4. D
    x = -a and y = -b 

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    Solution:

    Given two equations are: x a + y b =2   and axby= a 2 b 2  . We need to find the value of x and y.
    We have,
    x a + y b =2 bx+ay=2ab...(i)  
    and
    axby= a 2 b 2 ...(ii)  
    Multiply equation (i) by a and equation (ii) by b,
    abx+ a 2 y=2 a 2 b  
    abx b 2 y= a 2 b b 3  
    Now, subtracting the above equations we have,
    abx+ a 2 yabx+ b 2 y=2 a 2 b a 2 b+ b 3 a 2 y+ b 2 y= a 2 b+ b 3 y( a 2 + b 2 )=b( a 2 + b 2 ) y= b( a 2 + b 2 ) a 2 + b 2 y=b  
    Substituting the value of y in equation (i), we have,
    bx+ab=2ab bx=2abab bx=ab x= ab b x=a  
    Thus, the value of x&y   are a&b  .
    Therefore, option 1 is correct.
     
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