Question

Solve the pair of equations by reducing them to a pair of linear equations.
2/x + 3/y = 13
5/x - 4/y = -2 where x≠0, y≠0

Answer 1

Hi ,

It is given that ,

2/x + 3/y = 13 -----( 1 )

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

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

2a + 3b = 13 ----( 3 )

5a - 4b = -2 ----( 4 )

Do [ 4 × ( 3 ) + 3 × ( 4 ) ]

8a + 12b = 52

15a - 12b = -6
____________
23a = 46

a = 46/23

a = 2

substitute a = 2 in equation ( 3 ), we get

5 × 2 - 4b = -2

-4b = -2 - 10

b = ( -12 )/( -4 )

b = 3

Therefore ,

1/x = a = 2/1 => x = 1/2

1/y = b = 3/1 => y = 1/3

I hope this helps you.

: )