Recordemos que una ecuación es incompatible cuando el coeficiente de la variable es igual a 0
[tex]\boxed{\boldsymbol{\sf{\underset{=\ 0}{\underset{\downarrow}{A}}\ X =\underset{\neq\ 0}{\underset{\downarrow}{B}}}}}[/tex]
Entonces en el problema
[tex]\begin{array}{c}\sf{9x-7(x+1)+10=-Mx-6(x+2)+4}\\\\\sf{9x-7x-7+10=-Mx-6x-12+4}\\\\\sf{2x+3=-Mx-6x-8}\\\\\sf{2x+Mx+6x=-8-3}\\\\\sf{Mx+8x=-11}\\\\\sf{(M+8)x=-11}\\\\\sf{Para\ que\ sea\ incompatible\ se\ cumple\ que:}\\\\\sf{\underset{=\ 0}{\underset{\downarrow}{(M+8)}}x=-11}\\\\\sf{M+8=0}\\\\{\boxed{\boldsymbol{\sf{M=-8}}}\end{array}[/tex]
Nos piden
[tex]\sf{M^2=(-8)^2}\\\\\boxed{\boxed{\boldsymbol{\red{\sf{M^2=64}}}}}[/tex]
[tex]\boxed{\sf{{R}}\quad\raisebox{10pt}{$\sf{\red{O}}$}\!\!\!\!\raisebox{-10pt}{$\sf{\red{O}}$}\quad\raisebox{15pt}{$\sf{{G}}$}\!\!\!\!\raisebox{-15pt}{$\sf{{G}}$}\quad\raisebox{15pt}{$\sf{\red{H}}$}\!\!\!\!\raisebox{-15pt}{$\sf{\red{H}}$}\quad\raisebox{10pt}{$\sf{{E}}$}\!\!\!\!\raisebox{-10pt}{$\sf{{E}}$}\quad\sf{\red{R}}}\hspace{-64.5pt}\rule{10pt}{.2ex}\:\rule{3pt}{1ex}\rule{3pt}{1.5ex}\rule{3pt}{2ex}\rule{3pt}{1.5ex}\rule{3pt}{1ex}\:\rule{10pt}{.2ex}[/tex]
