x=10/y, 2y+3x=16

Question

x=10/y and 2y+3x=16

Answer 1

Replace x by 10/y in the equation 2y + 3x = 16:

 

2y + 30/y = 16

 

Multiply both sides by y:

 

2y² + 30 = 16y

 

Divide both sides by 2 and get 0 on one side:

 

y² - 8y + 15 = 0

 

(y-3)(y-5) = 0

 

y = 3 or y = 5

 

If y = 3, then x = 10/3

If y = 5, then x = 10/5 = 2

 

The two curves intersect at the points (10/3, 3) and (2, 5)