\( \begin{array}{c}3 x-y+z+7 w=13 \\ -2 x+y-z-3 w=-9 \\ -2 x+y-7 w=-8\end{array} \)

Step 1 ：1. Eliminate 'y' by adding Eq. (1) and Eq. (2): \\ \(x + 4w = 4\)

Step 2 ：2. Eliminate 'y' by adding Eq. (1) and Eq. (3): \\ \(x + 7z + 14w = 5\)

Step 3 ：3. Combine Eq. (4) and Eq. (5) to eliminate 'x' and solve for 'z': \\ \(3z + 10w = 1 \Rightarrow z = \frac{1 - 10w}{3}\)

Step 4 ：4. Substitute 'z' from Eq. (6) into Eq. (4) and solve for 'w': \\ \(x + 13\frac{1 - 10w}{3} = 4 \Rightarrow w = \frac{9}{37}\)

Step 5 ：5. Substitute 'w' into Eq. (6) to find 'z': \\ \(z = \frac{1 - 10 \cdot \frac{9}{37}}{3} = \frac{8}{37}\)

Step 6 ：6. Substitute 'z' and 'w' into Eq. (1) to find 'x': \\ \(3x - \frac{8}{37} + \frac{9}{37} + \frac{7 \cdot 9}{37} = 13 \Rightarrow x = 4\)

Step 7 ：7. Substitute 'z', 'w', and 'x' into Eq. (2) to find 'y': \\ \( - 2 \cdot 4 + y - \frac{8}{37} - \frac{3 \cdot 9}{37} = -9 \Rightarrow y = -2 \)