## Precalculus (6th Edition) Blitzer

Let us assume x and y to be the first and second lucky number: So, according to the first condition: $3x+6y=12$ $x+2y=4$ …… (I) Then, from the second condition: $x+2y=5$ …… (II) Then, from equation (I), $x+2y=4$ But from the second equation, $x+2y=5$ So, this twin is a liar. Thus, the speaking twin is a liar.