+564 Thanks so much for the help previously CPhill, it helped me with some other problems.
I'm stuck with this problem now however:
Solve for x and y: \(x^2+y^2=17 \)
\(y-1=x\)
There are two solutions: (x1, y1) and (x2, y2)
Evaluate x1+y1+x2+y2= ?
+129899 y - 1 = x → y = x + 1 (1)
x^2 + y^2 = 17 (2)
Subbing (1) into (2), we have
x^2 + ( x + 1)^2 = 17 simplify
x^2 + x^2 + 2x + 1 = 17
2x^2 + 2x - 16 = 0 divide through by 2
x^2 + x - 8 = 0
This will not factor.......using the quadratic formula, the two solutions for x are
[ -1 + sqrt(33)] / 2 and [ -1 - sqrt(33)] / 2
And y = x + 1
So.....when x = [ -1 + sqrt(33)] / 2 , y = x + 1 = [1 + sqrt(33)]/2
And, when x = [ -1 - sqrt(33)]/ 2 , y = x + 1 = [1 - sqrt(33)] / 2
And the sum of all these solutions is
[ -1 + sqrt(33)] /2 + [ -1 - sqrt(33)] / 2 + [1 + sqrt(33)]/2 + [1 - sqrt(33)] / 2 = (suprisingly, 0 !!! )
You can see why this is so from the following graph: https://www.desmos.com/calculator/8axms04lcy
The solution coorrdinates just "cancel" each other out when we sum them !!!!!!
