Question

Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations

x-y+4z=23
2x-y+z=-1
6x+4y+2y=-44

Answer 1

the answer is B. ( -6, -5, 6)

Explanation:

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Answer 2

I assume the third equation is supposed to be
`6x+4y+2z=-44`. We can divide both sides by 2 right away to simplify it a bit,
`3x+2y+z=-22`.

To start, the system in augmented-matrix form is

`\begin{bmatrix}1&-1&4&23\\2&-1&1&-1\\3&2&1&-22\end{bmatrix}`

Subtract 2 times row 1 from row 2, and 3 times row 1 from row 3:

`\begin{bmatrix}1&-1&4&23\\0&1&-7&-47\\0&5&-11&-91\end{bmatrix}`

Subtract 5 times row 2 from row 3:

`\begin{bmatrix}1&-1&4&23\\0&1&-7&-47\\0&0&24&144\end{bmatrix}`

Multiply row 3 by 1/24:

`\begin{bmatrix}1&-1&4&23\\0&1&-7&-47\\0&0&1&6\end{bmatrix}`

Add 7 times row 3 to row 2:

`\begin{bmatrix}1&-1&4&23\\0&1&0&-5\\0&0&1&6\end{bmatrix}`

Add row 2 and -4 times row 3 to row 1:

`\begin{bmatrix}1&0&0&-6\\0&1&0&-5\\0&0&1&6\end{bmatrix}`

Then the solution to the system is

`(x,y,z)=(-6,-5,6)`