1\x +1\y=2 and 1\y-1\x=6solve this equation by elimination and substit

1.	1\x +1\y=2 and 1\y-1\x=6solve this equation by elimination and substitution methodif you solve this question then i will you make brainlist
Answer» Given EQUATIONS : $\sf \dfrac{<klux>1</klux>}{x} + \dfrac{1}{y} = 2 \: \: \: ...(1)$ $\sf\dfrac{1}{y} - \dfrac{1}{x} = <klux>6</klux> \: \: \: ...(2)$ LET 1/x be u and 1/y be v equation 1 will become, $\sf u + v = 2 \: \: \: ...(3)$ equation 2 will become, $\sf v - u = 6 \: \: \: ...(4)$ by substituting both equation, PUT v = 6 + u in equation (3) $\dashrightarrow \sf u + v = 2$ $\dashrightarrow \sf u + (6 + u) = 2$ $\dashrightarrow \sf 2u = 2 - 6$ $\dashrightarrow \sf 2u = - 4$ $\dashrightarrow \sf u = - 2$ by putting u = -2 in equation (4) $\dashrightarrow \sf v - u = 6$ $\dashrightarrow \sf v - ( - 2) = 6$ $\dashrightarrow \sf v + 2 = 6$ $\dashrightarrow \sf v = 6 - 2$ $\dashrightarrow \sf v = 4$ we know, $\sf \dfrac{1}{x} = u$ $\sf \dfrac{1}{x} = - 2$ $\sf x = - \dfrac{1}{ 2}$ Similarly, $\sf \dfrac{1}{y} = v$ $\sf \dfrac{1}{y} = 4$ $\sf y = \dfrac{1}{4}$ Hence, $\boxed{ \sf x = - \dfrac{1}{ 2} } \sf \: \: \: and \: \: \: \boxed{ \sf y = \dfrac{1}{4} }$