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Let's solve the given system of equations step by step to find the value of \( y \).

### Given system:
\[
\text{Equation 1: } -4x + (-8) = 8
\]
\[
\text{Equation 2: } -4y + (-5x) = -6
\]

### Step 1: Solve for \( x \) from Equation 1
Simplify Equation 1:
\[
-4x - 8 = 8
\]
Add 8 to both sides:
\[
-4x = 16
\]
Now, divide both sides by -4:
\[
x = -4
\]

### Step 2: Substitute \( x = -4 \) into Equation 2
Substitute \( x = -4 \) into Equation 2:
\[
-4y - 5(-4) = -6
\]
Simplify:
\[
-4y + 20 = -6
\]
Subtract 20 from both sides:
\[
-4y = -26
\]
Now, divide both sides by -4:
\[
y = \frac{-26}{-4} = 6.5
\]

So, the value of \( y \) is 6.50 (rounded to the nearest hundredth).

Would you like more details or have any questions about this? Here are five related questions you might consider:

1. How do you verify if a solution to a system of equations is correct?
2. What other methods can be used to solve systems of equations, such as substitution or elimination?
3. How would the solution change if the constants in the equations were different?
4. Can you explain the impact of rounding when dealing with decimal solutions?
5. What happens when there is no solution or infinitely many solutions to a system of equations?

**Tip:** When solving systems of equations, always check your solution by plugging it back into both original equations to ensure it satisfies both.

-4x + (-8) = 8, -4y + (-5x) = -6. What is the value of y? Round to the nearest hundredth place.

Learn how to solve the system of linear equations -4x + (-8) = 8 and -4y + (-5x) = -6 to find the value of y. Detailed step-by-step solution with substitution method. Perfect for Grades 7-9 students looking to understand algebra and system of equations.

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