Question

Question 2 8 Find the coordinates of the points of intersection of the curve 1 and the line +9 [0] ​

Answer 1

point 1 = (3, 6)

point 2 = (24, -15)

Explanation:

8/x - 10/y = 1

x + y = 9

x = 9 - y

=>

8/(9-y) - 10/y = 1

8 - 10×(9-y)/y = 9 - y

-90/y + 10y/y = 1 - y

-90/y + 10 = 1 - y

-90 + 10y = y - y²

y² + 9y -90 = 0

the solution to a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case we use y instead of x.

a = 1

b = 9

c = -90

y = (-9 ± sqrt(81 - -360))/2 = (-9 ± sqrt(441))/2 =

= (-9 ± 21)/2

y1 = 12/2 = 6

y2 = -30/2 = -15

8/x - 10/6 = 1

8 - 10x/6 = x

8 - 5x/3 = x

24 - 5x = 3x

24 = 8x

x = 3

8/x - 10/-15 = 1

8/x + 2/3 = 1

8 + 2x/3 = x

24 +2x = 3x

24 = x