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10/x+y+2/x-y=4 15÷x+y-15/x-y=-2 |
| Answer» {tex}\\frac { 10 } { x + y } + \\frac { 2 } { x - y } = 4{/tex}{tex}\\frac { 15 } { x + y } - \\frac { 9 } { x - y } = - 2{/tex}.Putting\xa0{tex}\\frac 1{x+y}{/tex}=u and\xa0{tex}\\frac 1{x-y}{/tex}= v\xa0,the given equations{tex}10u +\xa02v= 4{/tex}........(i){tex}15u -\xa09v = -2{/tex}.......(ii)Multiplying (i) by 9\xa0and (ii) by 2 and adding them,{tex}\\Rightarrow{/tex}\xa0{tex}90 u + 18 v = 36\\ and\\ 30u - 18v = -4{/tex}{tex}\\Rightarrow 120u = 32{/tex}{tex}\\Rightarrow u = \\frac{4}{15}{/tex}Substituting u =\xa0{tex}\\frac{4}{15}{/tex} in (i), we get v =\xa0{tex}\\frac { 2 } { 3 }{/tex}{tex}\\Rightarrow \\frac { 1 } { x + y } = \\frac { 4 } { 15 } \\text { and } \\frac { 1 } { x - y } = \\frac { 2 } { 3 }{/tex}{tex}\\Rightarrow x + y = \\frac { 15 } { 4 }{/tex}\xa0.......(iii)and\xa0{tex}x - y = \\frac { 3 } { 2 }{/tex}\xa0......(iv)Adding (iii) and (iv),\xa0{tex}\\Rightarrow 2 x = \\frac { 21 } { 4 } \\Rightarrow x = \\frac { 21 } { 8 }{/tex}Substituting x ={tex}\\frac { 21 } { 8}{/tex}\xa0in (iii), we get\xa0{tex}y = \\frac { 9 } { 8 }{/tex}Hence, the solution is\xa0{tex}x = \\frac { 21 } { 8 } \\text { and } v = \\frac { 9 } { 8 }{/tex} | |