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+2z=-44

a. (-60, -53, 62)
b. (-6, -5, 6)
c. (-60, -5, -53)
d. ( -6, -5, -53)

Respuesta :

the answer is b it checks out for all of them

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Answer with explanation:

Writing the system of equation in Gauss Jordan form

[tex]\left[\begin{array}{cccc}1&-1&4&23\\2&-1&1&-1\\6&4&2&-44\end{array}\right]\\\\R_{2}\rightarrow R_{2}-2 R_{1} ,R_{3}\rightarrow R_{3}-6 R_{1} ,\left[\begin{array}{cccc}1&-1&4&23\\0&1&-7&-47\\0&10&-22&-182\end{array}\right]R_{3}\rightarrow R_{3}-10 R_{2}\\\\\left[\begin{array}{cccc}1&-1&4&23\\0&1&-7&-47\\0&0&48&288\end{array}\right][/tex]    

 Solving, it

4 8 z=288

[tex]z=\frac{288}{48}\\\\z=6\\\\y-7 z= -47\\\\y-7 \times 6= -47\\\\y=42-47\\\\y=-5\\\\x-y+4 z=23\\\\x-(-5)+4 \times 6=23\\\\x+5+24=23\\\\x=23-29\\\\x=-6[/tex]

⇒ (x, y, z)=(-6, -5, 6)

Option B