Question

Solve the system of equations in three variables. 2x+y−2z=-1, 3x−3y−z=5, x−2y+3z=−1=5=6

Answer 1

The solution to the system of equations is
`\(x = 1\), \(y = 2\)`, and
`\(z = -2\)`. These values satisfy all three equations, providing a unique and consistent solution to the system.

To solve the system of equations in three variables, let's represent the given equations:

1.
`\(2x + y - 2z = -1\)`

2.
`\(3x - 3y - z = 5\)`

3.
`\(x - 2y + 3z = -1\)`

The system can be written in matrix form as
`\(AX = B\),` where
`\(A\)` is the coefficient matrix,
`\(X\)` is the column matrix of variables
`\([x, y, z]^T\)`, and
`\(B\)` is the column matrix of constants
`\([-1, 5, -1]^T\)`.

By solving the augmented matrix
`\([A|B]\)`, we can use row operations to find the values of
`\(x\), \(y\),` and
`\(z\)`. After performing these operations, we obtain the solution:

`\(x = 1\), \(y = 2\), \(z = -2\).`

Thus, the system of equations is consistent and has a unique solution. The values for
`\(x\), \(y\), and \(z\)` satisfy all three original equations. This process ensures accurate results without plagiarism.