Solve the system using substitution. \( \left\{\begin{array}{l}-7 x-3 y=-45 \\ -5 x+y=-29\end{array}\right. \)

To solve the system using substitution, let's start with the second equation: \(-5x + y = -29\). We can express \(y\) in terms of \(x\): \(y = 5x - 29\). Now, substitute this expression for \(y\) into the first equation: \(-7x - 3(5x - 29) = -45\). Expanding that, we have: \(-7x - 15x + 87 = -45\). Combine like terms: \(-22x + 87 = -45\). Next, isolate \(x\): \(-22x = -45 - 87\) \(-22x = -132\) Now, divide both sides by -22: \(x = 6\). Now that we have \(x\), we can substitute it back to find \(y\). Using \(y = 5x - 29\): \(y = 5(6) - 29\) \(y = 30 - 29\) \(y = 1\). So, the solution to the system of equations is: \((x, y) = (6, 1)\).