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 equations, we can use substitution or elimination. We have two equations: 1. \( 2a - 3c = -6 \) 2. \( a + 2c = 11 \) From the second equation, we can express \( a \) in terms of \( c \): \[ a = 11 - 2c \] Now substitute \( a \) into the first equation: \[ 2(11 - 2c) - 3c = -6 \] \[ 22 - 4c - 3c = -6 \] \[ 22 - 7c = -6 \] Now, solve for \( c \): \[ -7c = -6 - 22 \] \[ -7c = -28 \] \[ c = 4 \] Now substitute \( c = 4 \) back into the equation for \( a \): \[ a = 11 - 2(4) \] \[ a = 11 - 8 \] \[ a = 3 \] Thus, the solution to the system of equations is: \( (a, c) = (3, 4) \) So the correct choice from the given options is \( (3,4) \).