Solve the system using the substitution method: \[ \begin{array}{l} 3 x+7 y=-2 \\ x=-5 y-6 \end{array} \] Enter your answer as an ordered pair.

Step 1 ：Understand the problem: We are given a system of two linear equations and we are asked to solve it using the substitution method. The solution will be an ordered pair (x, y) that satisfies both equations.

Step 2 ：Use the substitution method: The substitution method involves solving one of the equations for one variable and then substituting this expression into the other equation. Here, the second equation is already solved for x, so we can substitute this into the first equation.

Step 3 ：Substitute \(x = -5y - 6\) into the first equation: Substituting \(x = -5y - 6\) into the first equation gives: \(3(-5y - 6) + 7y = -2\), \(-15y - 18 + 7y = -2\), \(-8y - 18 = -2\), \(-8y = 16\), \(y = -2\)

Step 4 ：Substitute \(y = -2\) into the second equation: Substituting \(y = -2\) into the second equation gives: \(x = -5(-2) - 6\), \(x = 10 - 6\), \(x = 4\)

Step 5 ：Check the solution: Substitute \(x = 4\) and \(y = -2\) into the original equations to check the solution: \(3(4) + 7(-2) = 12 - 14 = -2\), \(4 = -5(-2) - 6 = 10 - 6 = 4\). Both equations are satisfied, so the solution is correct.

Step 6 ：\(\boxed{(x, y) = (4, -2)}\) is the final answer to the system of equations.