1. $\begin{cases}\lg x+\lg y=1 \\ x^{2}+x^{2}=29 \end{cases}$2. $\begin{cases}2^{3x+1}+2^{y-2}=3.2^{y+3x} \\ \sqrt{3x^{2}+1+xy}=\sqrt{x+1} \end{cases}$
3. $\begin{cases}(x^{4}+y).3^{y-x^{4}}=1 \\ 8(x^{4}+y)-6^{x^{4}-y}=0 \end{cases}$
4. $\begin{cases}2^{x}+2^{y}=12 \\ x+y=5 \end{cases}$