Find the solution to the system of equations. You can use the interactive graph below to find the solution. \( \left\{\begin{array}{l}-3 x-9 y=18 \\ 4 x+3 y=12\end{array}\right. \) \( x= \)

To solve the system of equations: \[ \begin{cases} -3x - 9y = 18 \quad \text{(1)} \\ 4x + 3y = 12 \quad \text{(2)} \end{cases} \] **Step 1: Eliminate \( y \)** First, let's eliminate \( y \) by making the coefficients of \( y \) in both equations equal in magnitude. - Multiply equation (2) by 3: \[ 3 \times (4x + 3y) = 3 \times 12 \\ 12x + 9y = 36 \quad \text{(3)} \] - Now, we have: \[ \begin{cases} -3x - 9y = 18 \quad \text{(1)} \\ 12x + 9y = 36 \quad \text{(3)} \end{cases} \] - Add equations (1) and (3) to eliminate \( y \): \[ (-3x - 9y) + (12x + 9y) = 18 + 36 \\ 9x = 54 \\ x = \frac{54}{9} \\ x = 6 \] **Step 2: Verify the Solution** Substitute \( x = 6 \) into equation (2): \[ 4(6) + 3y = 12 \\ 24 + 3y = 12 \\ 3y = -12 \\ y = -4 \] **Conclusion** The solution to the system of equations is: \[ x = 6 \quad \text{and} \quad y = -4 \] However, since you specifically requested the value of \( x \): **Answer:** \( x = 6 \)