Let's do this...using x - y = 6 ..... we can just rearrange it and say that y = x - 6
Now...in x^2 + y^2 = 26, let's substitute what we just got for y...so this gives us
x^2 + (x -6)^2 = 26 simplify
x^2 + x^2 - 12x + 36 = 26
2x^2 - 12x + 10 = 0 divide through by 2
x^2 - 6x + 5 = 0 factor
(x -5 ) ( x -1) = 0 so setting each factor to 0 , we find that x = 5 or x =1
And using y = x -6 when x =5 , y = -1 and when x = 1, y = -5
So..our solutions are (5, -1) and (1, -5)
This is just the intersection of a line with a circle...here's the graph....https://www.desmos.com/calculator/gv9ias9ptz