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## Solve the following simultaneous equations. ${7x -2y \over xy} = 5$  ${{8x + 7y} \over xy} =15$

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Sol.

Consider, ${7x -2y \over xy} = 5$

${7x \over xy } - {2y \over xy } = 5$

${-2 \over x} +{ 7 \over y} =5$

$-2({1 \over x}) + 7 ({1 \over y}) = 5$   ...(I)

Now consider

${{8x + 7y} \over xy }=15$

∴  ${8x \over xy} + {7y \over xy}=15$

∴ ${8 \over y} + {7 \over x} = 15$

∴ ${7 \over x} + {8 \over y} = 15$

∴ $7 ({1 \over x}) + 8({1 \over y})= 15$  ...(II)

Replace  $1 \over x$  by a  and  $1 \over y$ by b in equations (I) and (II), we get

–2a + 7b = 5 ...(III)

7a + 8b = 15 ...(IV)

Multiplying eq. (III) by 7 and eq. (IV) by 2

–14a + 49b = 35 ...(V)

14a + 16b  = 30 ...(VI)

Adding eq. (V) and (VI)

–14a + 49 b = 35

+ 14 a + 16 b = 30

65b = 65

b =1

Place b = 1 in eq. (III)

–2a + 7(1) = 5
∴  –2a + 7 = 5

∴ –2a = 5 – 7

∴ –2a = –2

∴ a =1

Resubstituting the values of a and b

${1 \over x} = 1$  and  ${1 \over y}=1$

∴ x =  1         ∴ y =  1

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

Linear equation in two variables August 04 , 2018 0 Comments 135 views