Calculate the coordinates of the intersection points of the functions: y = 8 / x; y = 6-x.

Y = 8 / X;

Y = 6 – X.

To determine the point of intersection of the graphs of functions, we equate the functions with each other.

(8 / X) = (6 – X).

We multiply both sides of the equality by X.

8 = X * (6 – X);

X ^ 2 – 6 * X + 8 = 0.

Let’s solve the quadratic equation.

D = b ^ 2 – 4 * a * c = (-6) ^ 2 – 4 * 1 * 8 = 36 – 32 = 4;

X1 = (6 – √4) / 2 * 1 = (6 – 2) / 2 = 4/2 = 2;

X2 = (6 + √4) / 2 * 1 = (6 + 2) / 2 = 8/2 = 4;

Y1 = 6 – 2 = 4;

Y2 = 6 – 4 = 2.

Answer: (2; 4), (4; 2).