When it is asking you to solve a system of equations, it means that it wants you to find the value of the variables, in this case, x and y.
3x + 2y = 1 -- equation 1
y = x - 12 -- equation 2
Put (equation 2)'s value of y into (equation 1)
3x + 2(x-12) = 1
3x + 2x - 24 = 1
5x - 24 = 1
5x = 25
x = 5 -- equation 3
Put (equation 3)'s values of x into (equation 2)
y = 5 - 12 = -7
Thus the solutions are x = 5 and y = -7 and we have solved the system of equations.
Hope that helped!