Question

Find the values of x and y​

Answer 1

`\:\:\:\:\:\:\:\:\:\:\therefore\bf{x=3\:and\:y=1}`

Solution

`\:\:\:\bf{(2^(x+y),\:3^(x-y))=(16,9)}`

`\sf{Here,}`

`\:\:\:\star\tt{\:\:2^(x+y)=16\:and\:3^(x-y)=9}`

`\sf{Solving,}`

`\:\:\:\implies\tt{\:\:2^(x+y)=16}`

`\:\:\:\implies\tt{\:\:2^(x+y)=2^4}`

`\:\:\:\implies\tt{\:\:x+y=4}`

`\:\:\:\bf{\:\:x=4-y-----(i)}`

`\sf{Solving,}`

`\:\:\:\implies\tt{\:\:3^(x-y)=9}`

`\:\:\:\implies\tt{\:\:3^(x-y)=3^2}`

`\:\:\:\bf{\:\:x-y=2-----(ii)}`

`\sf{Putting\:the\:value\:of\:(i)\:in\:(ii),}`

`\:\:\:\implies\tt{\:\:4-y-y=2}`

`\:\:\:\implies\tt{\:\:4-2y=2}`

`\:\:\:\implies\tt{\:\:-2y=2-4}`

`\:\:\:\implies\tt{\:\:\cancel{-}2y=\cancel{-}2}`

`\:\:\:\implies\tt{\:\:y=\frac{\cancel{2}}{\cancel{2}}}`

`\:\:\:\bf{\:\:y = 1}`

`\sf{Putting\:y = 1\:in\:(i),}`

`\:\:\:\implies\tt{\:\:x=4-1}`

`\:\:\:\bf{\:\:x = 3}`

`\:\:`