We have a system of two linear equations:

1. \( 3y = -2 \)
2. \( -9 = 2x - 7y \)

Let's solve this system step by step.

### Step 1: Solve the first equation for \( y \)
The first equation is \( 3y = -2 \). To solve for \( y \), divide both sides by 3:

\[
y = \frac{-2}{3}
\]

### Step 2: Substitute \( y = \frac{-2}{3} \) into the second equation
Now substitute \( y = \frac{-2}{3} \) into the second equation \( -9 = 2x - 7y \):

\[
-9 = 2x - 7 \left( \frac{-2}{3} \right)
\]

### Step 3: Simplify the equation
Simplify the term involving \( y \):

\[
-9 = 2x + \frac{14}{3}
\]

Multiply both sides of the equation by 3 to eliminate the fraction:

\[
-27 = 6x + 14
\]

### Step 4: Solve for \( x \)
Subtract 14 from both sides:

\[
-27 - 14 = 6x
\]

\[
-41 = 6x
\]

Now divide both sides by 6:

\[
x = \frac{-41}{6}
\]

### Final Answer:
The solution to the system of equations is:
\[
x = \frac{-41}{6}, \quad y = \frac{-2}{3}
\]

Would you like further details or explanations on any step?

Here are 5 related questions to expand your understanding:
1. How do you graph the two equations on the coordinate plane?
2. How can you verify the solution by substituting the values of \( x \) and \( y \) back into both equations?
3. What would happen if the system had no solution or infinitely many solutions?
4. How do you solve similar systems using substitution or elimination methods?
5. How does this system of equations relate to solving in matrix form?

**Tip**: Always double-check your solution by plugging the values back into the original equations to ensure they satisfy both.

Learn how to solve a system of linear equations with the example 3y = -2 and -9 = 2x - 7y. Follow a detailed step-by-step solution using substitution to find the values of x and y. This problem is ideal for students in Grades 8-10.

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