Answer
(1, -2) or (2, 1)
Work Step by Step
3x - y = 5 can be written as y = 3x - 5. Plug this into $x^{2} + y^{2} = 5$
$x^{2} + (3x - 5)^{2} = 5$
$x^{2} + 9x^{2} - 30x + 25 = 5$
$10x^{2} - 30x + 20 = 0$
Divide both sides by 10
$x^{2} - 3x + 2 = 0$
Factor
(x - 1)(x - 2) = 0
x - 1 = 0 or x - 2 = 0
x= 1 or 2
Plug x-values into y = 3x - 5
For x = 1: y = 3(1) - 5 = -2
For x = 2: y = 3(2) - 5 = 1
(1, -2) or (2, 1)
