https://file.aiquickdraw.com/mathbot/file/1726892402442if87rve3.jpg

Let's analyze and solve the two questions presented in the image.

### Question 4:
The equation is \(10 - 6y = 9\), and you are asked to solve for \(y\).

1. Subtract 10 from both sides:
   \[
   10 - 6y - 10 = 9 - 10
   \]
   Simplifying:
   \[
   -6y = -1
   \]

2. Divide both sides by \(-6\):
   \[
   y = \frac{-1}{-6} = \frac{1}{6}
   \]

Thus, the correct solution is \( y = \frac{1}{6} \).

### Question 5:
The equation is \(9 + 8y = 5y\), and you are asked to solve for \(y\).

1. Subtract \(5y\) from both sides:
   \[
   9 + 8y - 5y = 5y - 5y
   \]
   Simplifying:
   \[
   9 + 3y = 0
   \]

2. Subtract 9 from both sides:
   \[
   3y = -9
   \]

3. Divide both sides by 3:
   \[
   y = \frac{-9}{3} = -3
   \]

Thus, the correct solution is \( y = -3 \).

Let me know if you'd like any more details or if you have other questions! 

Here are five related questions to explore:
1. What happens when you multiply or divide both sides of an equation by a negative number?
2. How do you solve equations with variables on both sides?
3. Can you describe the importance of inverse operations in solving equations?
4. How would you solve an equation with fractions?
5. How do you check your solution in an equation?

**Tip:** Always simplify the equation step-by-step to avoid errors, and check your solution by plugging it back into the original equation.

Which of the following is the correct solution to 10 - 6y = 9 after solving for y? Which of the following is the correct solution to 9 + 8y = 5y after solving for y?

Learn how to solve the linear equations 10 - 6y = 9 and 9 + 8y = 5y with a detailed step-by-step guide. This problem covers essential algebraic concepts, including properties of equality and inverse operations. Suitable for students in Grades 7-8.

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