Question

solve the following pair of equation by reducing them to a pair of linear equation 5 by X + Y + 1 by x minus y equal to 2 10 by X + y + 3 by x minus y is equal to 5​

Answer 1

$\text{Given equations are}$

$\displaystyle\frac{5}{x+y}+\frac{1}{x-y}=2$

$\displaystyle\frac{10}{x+y}+\frac{3}{x-y}=5$

$\text{Take, }u=\frac{1}{x+y}\;\text{and}\;v=\frac{1}{x-y}$

$\text{The given equations become}$

$5u+v=2$ ........(1)

$10u+3v=5$ .......(2)

$\text{(1) {\times} 2}\implies$

$10u+2v=4$ ......(3)

$\text{(2)-(3) \implies }$

$\bf\,v=1$

$\text{(1) \implies }\,5u=1\implies\bf\,u=\frac{1}{5}$

$u=\frac{1}{5}\;\implies\,\frac{1}{x+y}=\frac{1}{5}$

$\implies\,x+y=5$......(4)

$v=1\;\implies\,\frac{1}{x-y}=1$

$\implies\;x-y=1$ .......(5)

$\text{Adding (1) and (2), we get}$

$2x=6$

$\implies\boxed{\bf\;x=3}$

$\text{(4)}\implies\,\boxed{\bf\;y=2}$

$\therefore\textbf{The solution is x=3 and y=2}$

Find more:

Solve: 6/x-1- 3/y-2=1, 5/x-1+1/y-2=2, where x is not 1 and y is not 2

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