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| 1. |
Solve x/a-y/b=0 and ax+by=a²+b² |
| Answer» {tex}\\frac { x } { a } - \\frac { y } { b } = 0{/tex}{tex} \\Rightarrow x = \\frac { a y } { b }{/tex}....................(i)ax + by = (a2\xa0+ b2) .......................(ii)Substituting (i) in (ii),we get{tex}a \\left( \\frac { a y } { b } \\right) + b y = \\left( a ^ { 2 } + b ^ { 2 } \\right){/tex}{tex}\\Rightarrow \\frac { a ^ { 2 } y } { b } + b y = \\left( a ^ { 2 } + b ^ { 2 } \\right){/tex}{tex}\\Rightarrow a ^ { 2 } y + b ^ { 2 } y = \\left( a ^ { 2 } b + b ^ { 3 } \\right){/tex}{tex}\\Rightarrow y \\left( a ^ { 2 } + b ^ { 2 } \\right) = b \\left( a ^ { 2 } + b ^ { 2 } \\right){/tex}{tex}\\Rightarrow y = b{/tex}Substituting in (i),we get{tex} x = \\frac { a b } { b }{/tex}\xa0⇒ x = a.So, solution of given equation is x = a and y = b. | |