What is the solution \( (a, c) \) to this system of linear equations? \( \begin{array}{l}2 a-3 c=-6 \\ a+2 c=11 \\ \left(-\frac{76}{7}, \frac{17}{7}\right) \\ (3,-4) \\ (3,4) \\ \left(\frac{87}{7},-\frac{5}{7}\right)\end{array} \)

To solve the system of linear equations: \[ \begin{cases} 2a - 3c = -6 \\ a + 2c = 11 \end{cases} \] **Step 1: Solve for one variable in terms of the other.** From the second equation: \[ a + 2c = 11 \\ \Rightarrow a = 11 - 2c \] **Step 2: Substitute this expression into the first equation.** \[ 2a - 3c = -6 \\ 2(11 - 2c) - 3c = -6 \\ 22 - 4c - 3c = -6 \\ 22 - 7c = -6 \] **Step 3: Solve for \( c \).** \[ -7c = -6 - 22 \\ -7c = -28 \\ c = \frac{-28}{-7} \\ c = 4 \] **Step 4: Substitute \( c \) back into the expression for \( a \).** \[ a = 11 - 2c \\ a = 11 - 2(4) \\ a = 11 - 8 \\ a = 3 \] **Solution:** \[ (a, c) = (3, 4) \] Among the provided options, the correct solution is **\( (3, 4) \)**.