I think the second equation should be x + 3y = -1.
System determinate:
System determinate is nothing but the co-efficient matrix
Therefore, co-efficient matrix is ![\left[\begin{array}{cc}1&3\\1&3\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%263%5C%5C1%263%5C%5C%5Cend%7Barray%7D%5Cright%5D)
x-determinate
x determinate is obtained by replacing the first column of the system determinate by solution column.
Therefore, x-determinate is ![\left[\begin{array}{cc}5&3\\-1&3\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%263%5C%5C-1%263%5C%5C%5Cend%7Barray%7D%5Cright%5D)
y-determinate
y determinate is obtained by replacing the second column of the system determinate by solution column.
Therefore, y-determinate is ![\left[\begin{array}{cc}1&5\\1&-1\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%265%5C%5C1%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D)