1] 2a + b = c + 32.
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2] 1 / 3 b + 2c = a + 9.
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3] (a + b) / 3 = c - 1.
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__________________| * Orden y simplificación del sistema dado :
1] 2a + b = c + 32.
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2] 1 / 3 b + 2c = a + 9.
| / * 3
3] (a + b) / 3 = c - 1.
| / * 3
__________________|
1] 2a + b - c = 32.
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2] b + 6c = 3a + 27.
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3] a + b = 3c - 3.
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_________________|
1] 2a + b - c = 32.
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2] - 3a + b + 6c = 27.
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3] a + b - 3c = - 3.
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__________________| * Resolución mediante Doble Reducción :
1° Reducción = = = = = = = = = = =
1] 2a + b - c = 32.
| / * 6
2] - 3a + b + 6c = 27.
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__________________|
12a + 6b - 6c = 192 - 3a + b + 6c = 27
4] 9a + 7b = 219
2] - 3a + b + 6c = 27.
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3] a + b - 3c = - 3.
| / * 2
__________________| - 3a + b + 6c = 27
2a + 2b - 6c = - 6
5] - a + 3b = 21
2° Reducción = = = = = = = = = = =
4] 9a + 7b = 219.
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5] - a + 3b = 21.
| / * 9
_______________|
9a + 7b = 219 - 9a + 27b = 189
34b = 408 .
/ : 34
b = 12 años ← Edad de Bárbara
4] 9a + 7b = 219
9a + 7(12) = 219
9a + 84 = 219
9a = 219 - 84
9a = 135 .
/ : 9
a = 15 años ← Edad de Ana
2] - 3a + b + 6c = 27 - 3(15) + 12 + 6c = 27 - 45 + 12 + 6c = 27 - 33 + 6c = 27
6c = 27 + 33
6c = 60 .
/ : 6
c = 10 años ← Edad de Carlos = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = .