\( C \left\{ \left. \begin{array} { c | l } { m + 2 n = 1 } \\ { - 3 m + n = - 10 } \end{array} \right. \begin{array} { l } { m = } \\ { n = } \end{array} \right. \)

Solve the system of equations \( m + 2n = 1; -3m + n = -10 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}m+2n=1\\-3m+n=-10\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}m=1-2n\\-3m+n=-10\end{array}\right.\) - step2: Substitute the value of \(m:\) \(-3\left(1-2n\right)+n=-10\) - step3: Simplify: \(-3+7n=-10\) - step4: Move the constant to the right side: \(7n=-10+3\) - step5: Add the numbers: \(7n=-7\) - step6: Divide both sides: \(\frac{7n}{7}=\frac{-7}{7}\) - step7: Divide the numbers: \(n=-1\) - step8: Substitute the value of \(n:\) \(m=1-2\left(-1\right)\) - step9: Substitute back: \(m=1+2\) - step10: Calculate: \(m=3\) - step11: Calculate: \(\left\{ \begin{array}{l}m=3\\n=-1\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}m=3\\n=-1\end{array}\right.\) - step13: Rewrite: \(\left(m,n\right) = \left(3,-1\right)\) La solución del sistema de ecuaciones es \( m = 3 \) y \( n = -1 \).