1. **Problem statement:** Solve the system of linear equations using row operations (Gaussian elimination). 2. **General approach:** We write the system as an augmented matrix and perform row operations to reach row echelon form or reduced row echelon form. 3. **Example:** Suppose the system is $$\begin{cases} a_{11}x + a_{12}y + a_{13}z = b_1 \\ a_{21}x + a_{22}y + a_{23}z = b_2 \\ a_{31}x + a_{32}y + a_{33}z = b_3 \end{cases}$$ 4. **Form the augmented matrix:** $$\left[\begin{array}{ccc|c} a_{11} & a_{12} & a_{13} & b_1 \\ a_{21} & a_{22} & a_{23} & b_2 \\ a_{31} & a_{32} & a_{33} & b_3 \end{array}\right]$$ 5. **Perform row operations:** - Swap rows if needed to get a nonzero pivot. - Multiply a row by a nonzero scalar. - Add or subtract multiples of one row to another to create zeros below pivots. 6. **Continue until the matrix is in row echelon form:** $$\left[\begin{array}{ccc|c} 1 & * & * & * \\ 0 & 1 & * & * \\ 0 & 0 & 1 & * \end{array}\right]$$ 7. **Back substitution:** Solve for variables starting from the last row upwards. 8. **Final solution:** Express $x$, $y$, and $z$ in terms of constants. *Note:* Since no specific system was given, this is the general method to solve by row operations.