Let's go through the problem step-by-step:

We are given the equation:

$2x - 3y = 9$

The goal is to solve for $y$ by isolating it on one side of the equation. The instructions ask to fill in the blanks for the steps provided.

Step 1: Subtract ____ from both sides of the equal.

To isolate $y$, we first need to get rid of the term involving $x$. So, we subtract $2x$ from both sides:

$2x - 3y - 2x = 9 - 2x$

This simplifies to:

$-3y = -2x + 9$

Step 2: Divide both sides by ____.

Now, to fully isolate $y$, divide both sides by $-3$ (since $y$ is multiplied by $-3$):

$y = \frac{-2x + 9}{-3}$

Simplifying the right-hand side:

$y = \frac{-2x}{-3} + \frac{9}{-3}$

$y = \frac{2x}{3} - 3$

Thus, the solution for $y$ is:

$y = \frac{2x}{3} - 3$

Answer:

• Step 1: Subtract $2x$ from both sides.
• Step 2: Divide both sides by $-3$.

Would you like more details, or do you have any questions?

Here are 5 related questions:

1. What does it mean to isolate a variable in an equation?
2. How do you know which term to subtract in step 1?
3. What are the rules for dividing both sides of an equation by a negative number?
4. How do you graph the equation $y = \frac{2x}{3} - 3$?
5. What happens if you don’t subtract the right term in the first step?

Tip: Always remember to flip the sign when dividing by a negative number to keep the equation consistent.