There are 35 rabbits and birds combined in one cage. There are 94 legs in the cage. How may rabbits and how many birds are there?

There are 35 rabbits and birds combined in one cage. There are 94 legs in the cage. How may rabbits and how many birds are there?

$$\begin{array}{lrcrcl} (1)& \quad \small{\text{ rabbits } & +& \small{\text{ birds }} &= & 35 \\\\ \hline \\ & \quad 4* \small{\text{ rabbits } &+& 2* \small{\text{ birds }} &=& 94 \quad | \quad :2\\\\ (2) & \quad 2* \small{\text{ rabbits } &+& \small{\text{ birds }} &=& 47 \\\\ \hline \\ (2)-(1): &2* \small{\text{ rabbits }-\small{\text{ rabbits } &+& \small{\text{ birds }} -\small{\text{ birds }} &=& 47-35\\\\ &\small{\text{ rabbits } } &+& 0 &=&12 \\\\ &\small{\text{ rabbits } }&& &=&12 \end{array}\\ \boxed{\small{\text{ rabbits } } =12 } \\ \begin{array}{lrcrcl} (1) & \small{\text{ rabbits } }&+& \small{\text{ birds }} &=& 35 \\ & 12 & + & \small{\text{ birds }} & = & 35 \qquad | \quad -12 \\ & & & \small{\text{ birds }} & = & 35-12 \\ & && \small{\text{ birds }} & = & 23 \end{array} \\ \boxed{birds = 23}$$