+564 Hey guys, I need some help with this problem:
Solve the system: {3x - y=6} {xy=24} There are two solutions: (x1, y1) and (x2, y2)
Evaluate: x1+y1+x2+y2= ?
+129899 3x - y = 6 (1)
xy = 24 → y = 24/x (2)
So..... substituting (2) into (1), we have
3x - 24/x = 6 multiply through by x
3x^2 - 24 = 6x re-arrange
3x^2 - 6x -24 = 0 divide through by 3
x^2 - 2x - 8 = 0 factor
( x - 4) ( x + 2) = 0 and setting each factor to 0, we have
x = 4 and x = -2
So.... y = 24/4 = 6 or.... y = 24/-2 = -12
And we have (4, 6) and ( -2, -12)
And the sum of these is just 10 + -14 = -4
+129899 3x - y = 6 (1)
xy = 24 → y = 24/x (2)
So..... substituting (2) into (1), we have
3x - 24/x = 6 multiply through by x
3x^2 - 24 = 6x re-arrange
3x^2 - 6x -24 = 0 divide through by 3
x^2 - 2x - 8 = 0 factor
( x - 4) ( x + 2) = 0 and setting each factor to 0, we have
x = 4 and x = -2
So.... y = 24/4 = 6 or.... y = 24/-2 = -12
And we have (4, 6) and ( -2, -12)
And the sum of these is just 10 + -14 = -4
