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3X - 2Y = 17 (Ecuacion 2)
3X = 2Y + 17
X = 2Y/3 + 17/3
Reemplazo X en la ecuacion (1)
[2^(2X - 3)]/[2^(3Y + 2)] = 2^8
[2^(2(2Y/3 + 17/3) - 3)]/[2^(3Y + 2)] = 2^8
[2^(4Y/3 + 34/3 - 3)]/[2^(3Y + 2)] = 2^8
[2^(4Y/3 + 34/3 - 3)]/[2^(3Y + 2)] = 2^8
[2^(4Y/3 + 25/3)]/[2^(3Y + 2)] = 2^8
[2^(4Y/3 + 25/3)]*1/[2^(3Y + 2)] = 2^8
[2^(4Y/3 + 25/3)]*[2^-(3Y + 2)] = 2^8
2^[(4Y/3 + 25/3) - (3Y + 2)] = 2^8
Aplicamos la siguiente propiedad:
a^f(x) = a^g(x)
f(x) = g(x)
[(4Y/3 + 25/3) - (3Y + 2)] = 8
4Y/3 + 25/3 - 3Y - 2 = 8
4Y/3 - 3Y + 25/3 - 2; 4Y/3 - 9Y/3 = -5Y/3
25/3 - 2 = 25/3 - 6/3 = 19/3
-5Y/3 + 19/3 = 8
-5Y + 19 = 24
19 - 24 = 5Y
-5 = 5Y
Y = -5/5
Y = -1
Rta: A