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 [tex]\left[\begin{array}{cc}1&3\\1&3\\\end{array}\right][/tex]
x-determinate
x determinate is obtained by replacing the first column of the system determinate by solution column.
Therefore, x-determinate is [tex]\left[\begin{array}{cc}5&3\\-1&3\\\end{array}\right][/tex]
y-determinate
y determinate is obtained by replacing the second column of the system determinate by solution column.
Therefore, y-determinate is [tex]\left[\begin{array}{cc}1&5\\1&-1\\\end{array}\right][/tex]
