Question

solve the following pair of equations by reducing them to a pair of linear equation.
5/x+y +1/x-y =2 and
10/x+y+3/x-y =5​

Answer 1

$\text{Given equations are}$

$\frac{5}{x+y}+\frac{1}{x-y}=2\;\text{and}$

$\frac{10}{x+y}+\frac{3}{x-y}=5$​

$\text{Take}$

$\frac{1}{x+y}=a\;\text{and}\;\frac{1}{x-y}=b$

$\text{Now, the given equations can be written as}$

$5a+b=2\;\text{and}\;10a+3b=5$

$10a+2b=4\;\text{and}\;10a+3b=5$

$\text{Subtracting, we get}$

$-b=-1$

$\implies\bf\;b=1$

$b=1\implies\;5a+1=2$

$\implies\;5a=1$

$\implies\bf\;a=\frac{1}{5}$

$\text{Now, we have}$

$x+y=5\;\text{and}\;x-y=1$

$\text{Adding, we get}$

$2x=6$

$\implies\;x=3$

$\text{and}\;y=2$

$\therefore\textbf{The solution is}$

$\boxed{\bf\;x=3\;\text{and}\;y=2}$

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Solve by elimination method class 10

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