Answer
(-3, -4) or (4, 3)
Work Step by Step
x - y = 1 can also be written as x = y + 1. Plug this into $x^{2} + y^{2} = 25$
$(y + 1)^{2} + y^{2} = 25$
Expand
$y^{2} + 2y + 1 + y^{2} = 25$
$2y^{2} + 2y + 1 = 25$
$2y^{2} + 2y - 24 = 0$
Divide both sides by 2
$y^{2} + y - 12 = 0$
Factor
(y - 3)(y + 4) = 0
y + 4 = 0 or y - 3 = 0
y = -4 or 3
Plug the y-values back into x = y + 1
For y = -4: x = -4 + 1 = -3
For y = 3: x = 3 + 1 = 4
(-3, -4) or (4, 3)
