Matrices & Systems · Hard problem

Three countries trade pairwise; let $a_{ij}$ denote country $i$'s exports to country $j$. The total trade between countries $1$ and $2$ is $a_{12}+a_{21}=90$, and between countries $1$ and $3$ is $a_{13}+a_{31}=70$. Country $1$'s combined exports to $2$ and $3$ exceed its combined imports from $2$ and $3$ by $8$. Also, country $1$ exports to country $2$ exactly twice what it exports to country $3$. Find $a_{12}$.