x-2y=1 x^2+y^2=13

$$\\x-2y=1\qquad (1a)\qquad x^2+y^2=13\qquad (2)\\
x=1+2y\\
x^2=1+4y^2+4y\qquad (1b)\\
sub\;1b\;into\;2\\
1+4y^2+4y+y^2=13\\
5y^2+4y-12=0\\
5y^2+10y-6y-12=0\\
5y(y+2)-6(y+2)=0\\
(5y-6)(y+2)=0\\

y=+6/5\;\;\;\;or\;\;\;\;y=-2$$

now sub thes y values back into 1a to find the corresponding x values.

you can finish it :)

 

https://www.desmos.com/calculator/g79i5h67l3

x-2y=1                        x^2+y^2=13

                                   x ^2 = 13-y^2

                                    x  = sqrt(13y-2)

sqrt(13y-2) = 1+2y    | quadrieren

13-y^2 = 1+4y+4y^2

5y^2+4y-12=0

y1= 1,2          y2= -2

x=1+2y         x1 = 3,4       x2 = -3