Use substitution to solve the system. \[ \begin{array}{c}x=3 y-6 \\ 5 x+4 y=-11\end{array} \]

To solve the system using substitution, we can start by using the first equation \( x = 3y - 6 \) and substituting it into the second equation. 1. Substitute \( x \) into the second equation: \[ 5(3y - 6) + 4y = -11 \] 2. Distribute the 5: \[ 15y - 30 + 4y = -11 \] 3. Combine like terms: \[ 19y - 30 = -11 \] 4. Add 30 to both sides: \[ 19y = 19 \] 5. Divide by 19: \[ y = 1 \] Now, substitute \( y = 1 \) back into the first equation to find \( x \): \[ x = 3(1) - 6 = 3 - 6 = -3 \] So, the solution to the system is \( x = -3 \) and \( y = 1 \). The solution set is \( (-3, 1) \).