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!