1.
From the second equation, we have b = 14 - a.
Substitute b = 14 - a into the first equation: a^2 + (14 - a)^2 = 100
Expand and simplify: a^2 + 196 - 28a + a^2 = 100
2a^2 - 28a + 96 = 0
Divide by 2: a^2 - 14a + 48 = 0
Factor: (a - 6)(a - 8) = 0
So, a = 6 or a = 8
If a = 6, b = 14 - 6 = 8
If a = 8, b = 14 - 8 = 6
Therefore, the solutions are (6,8) and (8,6).

2.
From the second equation, we have b = 49 - a.
Substitute b = 49 - a into the first equation: a^2 + (49 - a)^2 = 1681
Expand and simplify: a^2 + 2401 - 98a + a^2 = 1681
2a^2 - 98a + 720 = 0
Divide by 2: a^2 - 49a + 360 = 0
Factor: (a - 9)(a - 40) = 0
So, a = 9 or a = 40
If a = 9, b = 49 - 9 = 40
If a = 40, b = 49 - 40 = 9
Therefore, the solutions are (9,40) and (40,9).