Question

. Solve the pair of equations by reducing them to a pair of linear equations.


$\frac{2}{x } + \frac{3}{y } = 13 \\ \\ \frac{5}{x } - \frac{4}{y} = - 2$
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Answer 1

2/x+3/y=13

5/x-4/y=-2

Replacing 1/x by m and 1/y by n

Therefore,

2m+3n=13........(1)

5m-4n=-2..........(2)

Multiplying eq. (1) by 4 and (2) by 3 we get,

8m+12n=52............(3)

15m-12n=-6.............(4)

Adding (3) & (4), we get,

m=2 and n=3,

Now,

1/x=m

1/x=2

x=1/2

and 1/y=n

1/y=3

y=1/3

Therefore, (1/2, 1/3) are the roots of given equation.