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Solve the following simultaneous equations.
\({7 \over 2x+1}+{13 \over y+2}=27\) ;

\({13 \over 2x+1} + {7 \over y+2 } =33\)

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Sol:

\(7({1 \over 2x+1}) + 13({1 \over y+ 2})=27\)     ...(I) 

\(13({1 \over 2x +1})+ {7({1 \over y+2})}=33\)    ...(II)

Replace  \(1\over 2x+1\)  by a  and  \(1 \over y+2\) by b in  equations (I) and (II)

 we get,

7a + 13b = 27 ...(III)

13a + 7b = 33 ...(IV) 

[In the two equations above, the coefficients of x and y are interchanged so use ASA]

Adding eq. (III) and (IV)

    7a + 13 b = 27

+ 13a +7 b = 33

   20a  +20 b = 60

a + b = 3 ...(V)

Subtracting eq. (III) and (IV)

7a +13b = 27

13a +7 b = 33

(–)    (–)    (–)

–6a +6 b = –6

–a + b = –1     ...(VI)

Adding eq. (V) and (VI)

      a + b =3

+  –a + b = –1

            2b = 2

              b =1

Place b = 1 in eq. (V)

a + 1 = 3
∴ a = 3 – 1

∴ a =2

Resubstituting the values of a and b 

\({1 \over 2x+1 } =2\)   and   \({1 \over y+2} = 1\)

2x + 1 = \(1 \over 2\)   and   y + 2 = 1

\(2x={1\over 2}-1\)  and  y =1 – 2

∴ \(2x ={-1\over 2}\)   and ∴  y = –1

\(x={-1\over 4}\)

∴  (x, y) = \(({-1 \over 4}, -1)\)  is the required solutions.

Linear equation in two variables August 04 , 2018 0 Comments 27 views