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Solve the following simultaneous equations.

\({148\over x }+{231 \over y} = {527 \over xy} ;\) \({231 \over x}+ {148 \over y}={610 \over xy}\)

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Sol:

 Consider  \({148\over x }+{231 \over y} = {527 \over xy} ;\)

Multiplying throughout by xy 

\({148 \over x} (xy) + {231 \over y}(xy) = {527 \over xy}(xy)\)

148y + 231x = 527
∴  231x + 148y = 527 ...(I)

Now consider,

\({231 \over x} + {148 \over y}= {610 \over xy} \)

Multiplying throughout by xy 

\({231 \over x}(xy) + {148 \over y}(xy)= {610 \over xy}(xy)\)

∴ 231y + 148x = 610

 ∴ 148x + 231y = 610 ...(II) 

Adding eq. (I) and (II)

    231x + 148y = 527

+  148x + 231y = 610

    379x + 379y = 1137

x + y = 3 ...(III)    (dividing by 379)

Subtracting eq. (I) and (II)

     231x + 148y = 527

–   148x + 231y = 610

     (–)       (–)        (–)

       83x  –83 y  =  –83

           x – y = –1 ...(IV)   (Dividing by 83)

Adding eq. (III) and (IV)

    x + y =3

+  x – y = –1

   2x      =2

     x =1

Place x = 1 in eq. (III)

1 + y =3

y = 3 – 1

y =2
∴ (x, y) = (1, 2) is the required solutions.
 

 

Linear equation in two variables August 04 , 2018 0 Comments 20 views