Given the system of equations match the following items
x + 3y = 5
x - 3y = -1

options:
y-determinate
x-determinate
system determinate

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

x-determinate

x determinate is obtained by replacing the first column of the system determinate by solution column.

Therefore, x-determinate is

y-determinate

y determinate is obtained by replacing the second column of the system determinate by solution column.

Therefore, y-determinate is