Question

4/x+5/y=7, 5/x+4/y=13/2,Solve the given pair of equations by the method of elimination

Answer 1

Solution :

4/x + 5/y = 7 ---( 1 )

5/x + 4/y = 13/2 ---( 2 )

Let 1/x = a , 1/y = b

4a + 5b = 7 ---( 3 )

5a + 4b = 13/2 --( 4 )

[ 5 × ( 3 ) - 4 × ( 4 ) ]

20a + 25b = 35----( 5 )

20a + 16b = 26 ----( 6 )
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•••••••• 9b = 9

=> b = 9/9

=> b = 1

Put b = 1 in equation ( 3 ), we get

4a + 5 × 1 = 7

=> 4a = 7 - 5

=> 4a = 2

=> a = 2/4

=> a = 1/2

Therefore ,

1/x = a = 1/2

=> x = 2 ,

1/y = b = 1

=> y = 1

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