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a + b = 15 ---> a = 15 - b.
3(a) - 2(b) = 5
3a - 2b = 5.
reemplazando "a"
3(15 - b) - 2b = 5
45 - 3b - 2b = 5
45 - 5 = 3b + 2b
40 = 5b
8 = b.
Entonces sí b=8.
Y a + b = 15 ---> a + 8 = 15 ----> a = 15 - 8 ----> a = 7.
El número es ab = 78.