Let's solve the system of linear equations step by step:

The two equations are:

1. \(-2y - 9x = 5\)
2. \(0 = 5x + 9\)

### Step 1: Solve the second equation for \(x\)
We can rewrite the second equation as:

\[
5x + 9 = 0
\]

Solve for \(x\):

\[
5x = -9
\]
\[
x = -\frac{9}{5}
\]

### Step 2: Substitute \(x = -\frac{9}{5}\) into the first equation
Now substitute this value of \(x\) into the first equation:

\[
-2y - 9\left(-\frac{9}{5}\right) = 5
\]

Simplify:

\[
-2y + \frac{81}{5} = 5
\]

Multiply everything by 5 to eliminate the fraction:

\[
-10y + 81 = 25
\]

### Step 3: Solve for \(y\)
Subtract 81 from both sides:

\[
-10y = 25 - 81
\]
\[
-10y = -56
\]

Now divide by \(-10\):

\[
y = \frac{-56}{-10} = \frac{28}{5}
\]

### Final Solution:
So, the solution is:
\[
x = -\frac{9}{5}, \quad y = \frac{28}{5}
\]

Do you need more details on any step or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you solve a system of equations using the substitution method?
2. What is the elimination method for solving systems of equations?
3. How do you graphically represent a system of linear equations?
4. Can systems of equations have no solution or infinitely many solutions? Why?
5. How can systems of equations be applied to real-world problems?

**Tip:** When solving linear equations, always simplify the constants first to make the solution easier to handle.

Explore how to solve the system of linear equations -2y - 9x = 5 and 0 = 5x + 9 using the substitution method. This step-by-step solution covers key algebra concepts and is suitable for students in Grades 8-10.

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