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2/Y + 2/Z = 3/2...Ec. (2)
1/X + 4/Z = 4/3...Ec. (3)
Restando Ec. (1) menos Ec. (2):
3/X + 2/Y - (2/Y + 2/Z) = 2 - 3/2
3/X + 2/Y - 2/Y - 2/Z = 1/2
3/X - 2/Z = 1/2...Ec.(4)
Multiplicando Ec. (4) por 2 y sumando Ec. (3):
2*(3/X - 2/Z) + (1/X + 4/Z) = 2*(1/2) + 4/3
6/X - 4/Z + 1/X + 4/Z = 1 + 4/3
7/X = 7/3
X = 3
Reemplazando en Ec. (1):
3/(3) + 2/Y = 2
1 + 2/Y = 2
2/Y = 1
Y = 2
Reemplazando en Ec. (2):
2/(2) + 2/Z = 3/2
1 + 2/Z = 3/2
2/Z = 3/2 - 1
2/Z = 1/2
Z = 4
Por lo tanto:
X = 3 ; Y = 2 ; Z = 4.
Nota:
Como ves, se resuelve de la misma forma que cuando las variables son los numeradores.