Question

solve the pair equations
$\frac{2}{x} + \frac{3}{y} = 13 \\ \\ \frac{5}{x} + \frac{4}{y} = - 2$

Answer 1

Hay


Let us write the given pair of equations as

$2 (\frac{1}{x} ) + 3( \frac{1}{y} ) = 13..........1$


$5( \frac{1}{x} ) - 4( \frac{1}{y} ) = - 2..........2$



These equations are not form ax+by+c=0. However if we substitute

1/x =p and 1/y =q in equations (1) and (2) we get

2p +3q =13............(3)
5p -4q =-2.............(4)

so, we have expressed the equation as a pair of linear equations. Now, you can use any methods to solve these equations, and get
p = 2,q=3.

You know that p = 1/x and q = 1/y

substitute the value of p and q to get

1/x = 2, I.e., x =1/2 and 1/y = 3 i.e., y =1/3

By substituting x = 1/2 and y = 1/3 in the given equation, we find that both the equation are satisfied.


I hope it's help you

Regards @sangela####

Answer 2

These equations are not form ax+by+c=0. However if we substitute




1/x =p and 1/y =q in equations (1) and (2) we get



2p +3q =13

5p -4q =-2



so, we have expressed the equation as a pair of linear equations. Now, you can use any methods to solve these equations, and get
p = 2,q=3.



You know that p = 1/x and q = 1/y



substitute the value of p and q to get



1/x = 2, I.e., x =1/2 and 1/y = 3 i.e., y =1/3



I hope it's help you