$A = 1$, $B = 2$ , $C = 10$, $D = 12$
Există $6$ perechi distincte de numere reale cu proprietăţile cerute: $(0.25,0.375)$, $(0.5,0.25)$, $(0.75,0.125)$, $(0.25,0.875)$, $(0.5,0.75)$ si $(0.75,0.625)$.

<tex> A \cdot X + B \cdot Y = 1 \cdot 0.25 + 2 \cdot 0.375 = 1 si C \cdot X + D \cdot Y = 10 \cdot 0.25 + 12 \cdot 0.375 = 7</tex>
<tex> A \cdot X + B \cdot Y = 1 \cdot 0.5 + 2 \cdot 0.25 = 1 si C \cdot X + D \cdot Y = 10 \cdot 0.5 + 12 \cdot 0.25 = 8</tex>
<tex> A \cdot X + B \cdot Y = 1 \cdot 0.75 + 2 \cdot 0.125 = 1 si C \cdot X + D \cdot Y = 10 \cdot 0.75 + 12 \cdot 0.125 = 9</tex>
<tex> A \cdot X + B \cdot Y = 1 \cdot 0.25 + 2 \cdot 0.875 = 2 si C \cdot X + D \cdot Y = 10 \cdot 0.25 + 12 \cdot 0.875 = 13</tex>
<tex> A \cdot X + B \cdot Y = 1 \cdot 0.5 + 2 \cdot 0.75 = 2 si C \cdot X + D \cdot Y = 10 \cdot 0.5 + 12 \cdot 0.75 = 14</tex>
<tex> A \cdot X + B \cdot Y = 1 \cdot 0.75 + 2 \cdot 0.625 = 2 si C \cdot X + D \cdot Y = 10 \cdot 0.75 + 12 \cdot 0.625 = 15</tex>
 

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