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Tcecarenko [31]
2 years ago
15

Find the values of x and y​

Mathematics
2 answers:
valentina_108 [34]2 years ago
7 0

Answer:

x = 3, y = 1

Step-by-step explanation:

2 raised to what power gives you 16?

2*2*2*2 = 16 so 2^4

3 raised to what power gives you 9?

3*3 = 9 so 3^2

the exponent cannot be negative so x has to be greater than y and x cannot be the same as y otherwise you will get a 0.

x = 3 , y = 1

2^(3+1) = 2^4 = 16

3^(3-1) = 3^2 = 9

rewona [7]2 years ago
3 0

\:\:\:\:\:\:\:\:\:\:\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}

\:\:

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