Real numbers $x$ and $y$ satisfy the equation $x^2 + y^2 = 10x - 6y - 34$. what is $x+y$?

2

Step-by-step explanation:

The equation can be rewritten as ...

... (x -5)² + (y +3)² = 0 . . . . . . a circle of radius 0 centered at (5, -3)

This is the equation of the point (5, -3). So, ...

... x + y = 5 - 3 = 2

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )

x = 3 ± √(5+y)