for the first one, you could just use basic substitution.
You know y = x - 1, so fill x - 1 for y in the second equation:
x^2 + (x - 1)^2 = 25
Foil the (x - 1)^2: x^2 + (x^2 -2x + 1) = 25
Simplify the LHS: 2x^2 -2x + 1 = 25
Get a quadratic equation: 2x^2 -2x -24 = 0
Divide both sides by 2: x^2 - x - 12 = 0
Factor it, getting: (x - 4)(x + 3) = 0
Solve for x, which obviously are the two x values of the two coordinates.
When you get the two x values, fill it in y = x - 1 to get the two y coordinates.
There ya go!