https://file.aiquickdraw.com/mathbot/file/17273794452213h7q5gzq.jpg

The system of linear equations provided in the image is:

\[
\begin{cases}
3x + 9y = 3 \\
9x + 6y = 2
\end{cases}
\]

Let's solve this system using the method of elimination or substitution.

### Step 1: Simplify the Equations

First, simplify each equation if possible:

1. Divide the first equation by 3:

   \[
   x + 3y = 1
   \]

2. Divide the second equation by 3:

   \[
   3x + 2y = \frac{2}{3}
   \]

Now, the simplified system is:

\[
\begin{cases}
x + 3y = 1 \\
3x + 2y = \frac{2}{3}
\end{cases}
\]

### Step 2: Use Substitution or Elimination

Let's solve this using substitution. From the first equation:

\[
x = 1 - 3y
\]

Substitute \( x = 1 - 3y \) into the second equation:

\[
3(1 - 3y) + 2y = \frac{2}{3}
\]

Simplify this:

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

\[
-7y = \frac{2}{3} - 3
\]

\[
-7y = \frac{2}{3} - \frac{9}{3}
\]

\[
-7y = -\frac{7}{3}
\]

\[
y = \frac{1}{3}
\]

### Step 3: Find \( x \)

Now substitute \( y = \frac{1}{3} \) into \( x = 1 - 3y \):

\[
x = 1 - 3\left(\frac{1}{3}\right)
\]

\[
x = 1 - 1 = 0
\]

### Solution

The solution to the system is:

\[
x = 0, \quad y = \frac{1}{3}
\]

Would you like a detailed breakdown of any specific step? Here are some related questions:

1. How can we verify the solution by plugging values back into the original equations?
2. What are other methods to solve this system, such as using matrices?
3. Can this system be solved graphically? What does the solution represent on a graph?
4. What happens if the system has no solution or infinitely many solutions?
5. How can we interpret these equations in a real-world context?

**Tip:** Always simplify equations when possible—it makes the calculations easier and less prone to errors!

Solve the system of linear equations: 3x + 9y = 3 and 9x + 6y = 2

Learn how to solve the system of linear equations 3x + 9y = 3 and 9x + 6y = 2 using substitution and elimination methods. This problem covers essential algebra concepts suitable for students in Grades 8-10.

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