James has a certain amount of money. If he buys $3$ pens and $2$ pencils, he will have $\$2$ left over. If he buys $2$ pens and $3$ pencils, he will have $\$6$ left over. If Judith arrives with the same amount of money as James, together they can buy $6$ of each and spend all their money. If $a$ is the cost of one pen and $b$ is the cost of one pencil, compute the ordered pair $(a, b)$.