What is the solution set of x2 + y2 = 26 and x - y = 6? A. { (5, - 1), (-5, 1) } B. { (1, 5), (5, 1) } C. { (-1, 5), (1, - 5) } D. { (5, - 1), (1, - 5) }.

He two equations given are

x^2 + y^2 = 26

And

x - y = 6

x = y + 6

Putting the value of x from the second equation to the first equation, we get

x^2 + y^2 = 26

(y + 6) ^2 + y^2 = 26

y^2 + 12y + 36 + y^2 = 26

2y^2 + 12y + 36 - 26 = 0

2y^2 + 12y + 10 = 0

y^2 + 6y + 5 = 0

y^2 + y + 5y + 5 = 0

y (y + 1) + 5 (y + 1) = 0

(y + 1) (y + 5) = 0

Then

y + 1 = 0

y = - 1

so x - y = 6

x + 1 = 6

x = 5

Or

y + 5 = 0

y = - 5

Again x = 1

So the solutions would be (-1, 5), (1, - 5). The correct option is option "C".