https://file.aiquickdraw.com/mathbot/file/1727404790073r8ne54t3.jpg

The image contains a system of linear equations:

1. \( 8x + 3y = 4 \)
2. \( -6x - 3y = -9 \)

Let's solve this system using the elimination method, as it seems suitable due to the matching coefficients of \( y \).

**Step-by-step solution:**

1. **Add the two equations together** to eliminate \( y \):

\[
(8x + 3y) + (-6x - 3y) = 4 - 9
\]

\[
(8x - 6x) + (3y - 3y) = -5
\]

\[
2x = -5
\]

2. **Solve for \( x \):**

\[
x = \frac{-5}{2} = -2.5
\]

3. **Substitute \( x = -2.5 \) into the first equation** to find \( y \):

\[
8(-2.5) + 3y = 4
\]

\[
-20 + 3y = 4
\]

\[
3y = 4 + 20
\]

\[
3y = 24
\]

\[
y = \frac{24}{3} = 8
\]

The solution is:

\[
x = -2.5, \quad y = 8
\]

If you have any further questions or need more details, feel free to ask!

**Relative Questions:**
1. How do you solve a system of equations using substitution?
2. What are the conditions for a system of equations to have no solution?
3. Can you explain how to graphically solve a system of linear equations?
4. How would the solution change if the coefficients of \( y \) were not opposites?
5. What are some common real-life applications of solving systems of equations?

**Tip:** Always check your solution by plugging the values back into the original equations to verify the correctness.

Solve the system of equations: 8x + 3y = 4 and -6x - 3y = -9

Learn how to solve a system of linear equations using the elimination method. This step-by-step solution covers the system of equations 8x + 3y = 4 and -6x - 3y = -9, suitable for Grades 8-10.

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