Question : If $2^x+3^y=17$ and $2^{x+2}-3^{y+1}=5$, then:
Option 1: $x= 1, y = 3$
Option 2: $x = 3, y = 3$
Option 3: $x = 3, y = 2$
Option 4: $x = 1, y = 2$
Answer (1)
23rd Jan, 2024
Correct Answer: $x = 3, y = 2$
Solution :
$2^x+3^y=17$
$2^{x+2}-3^{y+1}=5$
By trial and error method,
When $y = 2, x= 3$
$2^3+3^2=8+9=17$
$2^{3+2}-3^{2+1}=32–27=5$
Hence, the correct answer is $x = 3 $ and $y = 2$.
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