Solve $16x+9=9y-2x$ for $y$.

The solution for y is y = 2x + 1

Step-by-step explanation:

* Lets explain how to solve an equation for one of the variables

- We need to solve the equation 16x + 9 = 9y - 2 x for y

- That means we want to find y in terms of x and the numerical term

- the equation has two sides, one side contains x and numerical term

and the other side contains y and x

- We need to separate y in one side, and other term in the other side

* Lets do that

∵ 16x + 9 = 9y - 2x

- Add 2x to both sides to cancel - 2x from the right side

∴ 16x + 2x + 9 = 9y - 2x + 2x

- Add like terms in each side

∴ 18x + 9 = 9y

- Divide each term by the coefficient of y ⇒ (:9)

∴ (18 : 9) x + (9 : 9) = (9 : 9) y

∴ 2x + 1 = y

- Switch the two sides

∴ y = 2x + 1

* The solution for y is y = 2x + 1