(1 point) Linear System - Three Variables Solve the following system of equations using Gaussian elimination method. If there are no solutions, type "N" for both x, y and z. If there are infinitely many solutions, type "z" for z, and expressions in terms of z for x and y. 6x + 8y + 72 = -3 - 3x + 6y + 6z = 5 2x – 9y – 32 = 7

Answer:[tex]x=\frac{-363}{70}[/tex] ≈ -5.1857[tex]y=\frac{-192}{35}[/tex] ≈ -5.4857[tex]z=\frac{313}{84}[/tex] ≈ 3.7262Step-by-step explanation:Rewrite the equation system as:[tex]6x+8y=-75[/tex][tex]-3x+6y+6z=5[/tex][tex]2x-9y=39[/tex]Now, write the system in its augmented matrix form:[tex]\left[\begin{array}{cccc}6&8&0&-75\\-3&6&6&5\\2&-9&0&39\end{array}\right][/tex] applying row reduction process to  its associated augmented matrix: Swap R1 and R3, and then Swap R1 and R2:[tex]\left[\begin{array}{cccc}-3&6&6&5\\2&-9&0&39\\6&8&0&-75\end{array}\right][/tex]R3+2R1[tex]\left[\begin{array}{cccc}-3&6&6&5\\2&-9&0&39\\0&20&12&-65\end{array}\right][/tex]3R2+2R1[tex]\left[\begin{array}{cccc}-3&6&6&5\\0&-15&12&127\\0&20&12&-65\end{array}\right][/tex]15R3+20R2[tex]\left[\begin{array}{cccc}-3&6&6&5\\0&-15&12&127\\0&0&420&1565\end{array}\right][/tex]Now we have a simplified system:[tex]-3x+6y+6z=5\\0-15y+12z=127\\0+0+420z=1565[/tex][tex]-3x+6y+6z=5\hspace{5 mm}(1)\\0-15y+12z=127\hspace{3 mm}(2)\\0+0+420z=1565\hspace{3 mm}(3)[/tex]From (3):[tex]z=\frac{313}{84}[/tex] (4)Replacing (4) in (2)[tex]y=\frac{-192}{35}[/tex] (5)Finally replacing (5) and (4) in (1)[tex]x=\frac{-363}{70}[/tex]