Question

If (5x-y) varies directly as (2x+3y) which is always a constant?

Answer 1

whst are the options

Answer 2

A) x+y, B) x-y, C) xy, D)x/y

Answer 3

(5x-y) varies directly as (2x+3y)
means there is a constant, we will call it k, so that
5x-y= k(2x+3y)

if you distribute the k on the right side, you get
5x -y =2kx +3k y
collect terms

5x-2kx = 3k y + y
factor out x on the left side, and factor you y on the right side

(5-2k) x = (3k+1) y

Answer 4

notice that in
(5-2k) x = (3k+1) y

that 5-2k is a constant number. in other words, k is a fixed number and 5-2k will also be some number that does not change.

same for 3k+1

if we divide both sides by (5-2k) we get

x= (3k+1)/(5-2k) y

divide both sides by y
\[ \frac{x}{y}= \frac{3k+1}{5-2k} \]

Answer 5

Thanks