Correct option is (A) (3, 2)
\(2^x+3^y=17\) _________(1)
and \(2^{x+2} - 3^{y+1}=5\)
\(\Rightarrow\) \(2^2.2^x-3.3^y=5\)
\(\Rightarrow\) \(4.2^x-3.3^y=5\) _________(2)
Let \(2^x=X\;\&\;3^y=Y\)
Then equations (1) & (2) converts to
X + Y = 17 _________(3)
and 4X - 3Y = 5 _________(4)
Put Y = 17 - X from (3) into equation (4), we get
4X - 3 (17 - X) = 5
\(\Rightarrow\) 4X - 51 + 3X = 5
\(\Rightarrow\) 7X = 5+51 = 56
\(\Rightarrow\) X = \(\frac{56}7\) = 8
\(\therefore\) Y = 17 - X
= 17 - 8 = 9 (From (3))
\(\therefore\) X = 8
\(\Rightarrow\) \(2^x=8=2^3\)
\(\Rightarrow\) x = 3
and Y = 9
\(\Rightarrow\) \(3^y=9=3^2\)
\(\Rightarrow\) y = 2
Hence, (x, y) = (3, 2)
