https://file.aiquickdraw.com/mathbot/file/1727176838030thg1m6ff.jpg

The system of equations from the image is:

\[
\begin{cases}
6a - 2b = 9 \\
6a + 3b = 4
\end{cases}
\]

Let's solve this system using the elimination method.

1. **Step 1: Eliminate \(a\)**  
   Subtract the second equation from the first to eliminate \(a\).

\[
(6a - 2b) - (6a + 3b) = 9 - 4
\]

Simplifying this:

\[
6a - 2b - 6a - 3b = 5
\]

\[
-5b = 5
\]

Solving for \(b\):

\[
b = -1
\]

2. **Step 2: Substitute \(b = -1\) into one of the original equations**  
   Use the first equation \(6a - 2b = 9\):

\[
6a - 2(-1) = 9
\]

This simplifies to:

\[
6a + 2 = 9
\]

Subtract 2 from both sides:

\[
6a = 7
\]

Solve for \(a\):

\[
a = \frac{7}{6}
\]

### Final Solution:
The solution to the system is:

\[
a = \frac{7}{6}, \quad b = -1
\]

Would you like more details or have any questions? Here are some related problems for further practice:

1. Solve the system using substitution: \(3a - 4b = 5\) and \(2a + b = 3\).
2. Solve the system: \(7x - 3y = 12\) and \(x + 2y = 5\).
3. Solve the system graphically: \(y = 2x - 3\) and \(y = -x + 4\).
4. Find the values of \(x\) and \(y\) in \(5x + 2y = 20\) and \(x - y = 4\).
5. Solve using matrices: \(2a + 3b = 5\) and \(a - 4b = -2\).

### Tip:
Always double-check your substitution after solving for one variable to ensure there are no arithmetic errors.

Solve the system of equations: 6a - 2b = 9 and 6a + 3b = 4.

Learn how to solve the system of linear equations 6a - 2b = 9 and 6a + 3b = 4 using the elimination method. This step-by-step guide covers key algebraic concepts and provides a clear solution for students in Grades 8-10.

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