MathematicsSolve the following pair of equations by reducing them to a pair of linear equations: 1(3x+y)+1(3x-y)=34; 12(3x+y)-12(3x-y)=-18.

Solve the following pair of equations by reducing them to a pair of linear equations: 1(3x+y)+1(3x-y)=34; 12(3x+y)-12(3x-y)=-18.


  1. A
    x=2,y=7
  2. B
    x=5,y=0
  3. C
    x=1,y=1
  4. D
    x=2,y=3 

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    Solution:

    Given equations are, 1(3x+y)+1(3x-y)=34; 12(3x+y)-12(3x-y)=-18.
    Let 1(3x+y)=a and 1(3x-y)=b.
    Then, a+b=34
    4a+4b=3………….(1)
    Also, a2-b2=-18.
    a-b2=-18
    a-b=-14
    4a-4b=-1……………..(2)
    Adding equation (1) and equation (2) we get,
    8a=2
    a=14
    Substituting a=14 in equation (1) we get,
    4(14) +4b=3
    4b=2
    b=12
    Then, 13x+y=14.
    3x+y=4…………..(3)
    And 13x-y=12.
    3x-y=2………………(4)
    Adding equation (3) and equation (4)  we get,
    6x=6
    x=1
    Substituting x=1 in equation (3) we get,
    3×1+y=4
    y=1
    Therefore, option (3) is correct.
     
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