Problem

$\left\{\begin{array}{l}x-2 y+z=1 \\ y+2 z=-9 \\ x+y+3 z=-14\end{array}\right.$

Solution

Step 1 :Given the system of linear equations: \(\begin{cases} x-2y+z=1 \\ y+2z=-9 \\ x+y+3z=-14 \end{cases}\)

Step 2 :We can represent this system in matrix form as: \(\begin{bmatrix} 1 & -2 & 1 \\ 0 & 1 & 2 \\ 1 & 1 & 3 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ -9 \\ -14 \end{bmatrix}\)

Step 3 :Solving this system of equations, we find the solution to be: \(x = -2, y = -3, z = -3\)

Step 4 :Final Answer: \(\boxed{x = -2, y = -3, z = -3}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8672/

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