Como puedo resolver esta inecuación3x + 4y>99x + 12y> - 27?

Lo resolvemos por el método de sustitución : Tenemos que despejar la primera ecuación a "x" :

<img src="https://tex.z-dn.net/?f=%5Ccheckmark%2013x%2B4y%5C%20%5Ctextgreater%20%5C%209%20%5C%5C%20%5C%5C%203x%5C%20%5Ctextgreater%20%5C%209-4y%20%5C%5C%20%5C%5C%20%5Cboxed%7Bx%5C%20%5Ctextgreater%20%5C%20%5Cdfrac%7B9-4y%7D%7B3%7D%7D%20%5C%5C%20%5C%5C%24%20Sustituimos%20este%20valor%20en%20la%20segunda%20ecuaci%5C%27on%3A%20" />

<img src="https://tex.z-dn.net/?f=%5Ccheckmark%209x%2B12y%5Ctextgreater-27%20%5C%5C%20%5C%5C%209%5Cleft%28%5Cdfrac%7B9-4y%7D%7B3%7D%5Cright%29%2B12y%5Ctextgreater-27%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cleft%28%5Cdfrac%7B9%289-4y%29%7D%7B3%7D%5Cright%29%2B12y%5Ctextgreater-27%20%5C%5C%20%5C%5C%20%5Cleft%28%5Cdfrac%7B%2881-36y%29%7D%7B3%7D%5Cright%29%2B12y%5Ctextgreater-27%20%5C%5C%20%5C%5C%20%5C%5C%20%24Multiplicamos%20a%20toda%20la%20ecuaci%5C%27on%20por%20%5Ctextbf%7B3%7D%2C%20para%20poder%20sacar%20a%20los%20%5C%5C%20n%5C%27umeros%20de%20la%20fracci%5C%27on%3A%20%5C%5C%20%5C%5C%20%5Cnot%7B3%7D%5Cleft%28%5Cdfrac%7B%2881-36y%29%7D%7B%5Cnot%7B3%7D%7D%5Cright%29%2B3%2812y%29%5Ctextgreater3%28-27%29%20%5C%5C%20%5C%5C%2081-%5Cnot%7B36y%7D%2B%5Cnot%7B36y%7D%5Ctextgreater-81%20%5C%5C%20%5C%5C%20%5Cboxed%7B81%5Ctextgreater-81%7D%20" />

<img src="https://tex.z-dn.net/?f=%7B%24Podemos%20darnos%20cuenta%20que%20en%20ecuaci%5C%27on%20no%20importara%20el%20valor%20de%20%5Ctextbf%7By%7D%20%5C%5C%20%20siempre%20y%20cuando%20sea%20un%20valor%20%5Ctextbf%7Bnegativo%7D%2C%20es%20decir%2C%20que%20al%20proceso%20de%20%20%5C%5C%20comprobar%20las%20igualdades%20no%20afectar%5C%27a%20la%20ecuaci%5C%27on%2C%20siempre%20ser%5C%27a%20%5C%5C%20verdadera%20la%20ecuaci%5C%27on%20%20%20%20%20%5C%5C%20%20%5C%5C%20Asi%20que%20el%20valor%20de%20%5Ctextbf%7By%7D%20sera%20de%20%5Ctextbf%7B-81%7D.%20%5C%5C%20%5C%5C%20%5Cboxed%7B%5Ctextbf%7Bx%3D%20-81%7D%7D%20%5C%5C%20%5C%5C%203x%2B4y%5Ctextgreater9%20Comprobaci%5C%27on%3A" />

<img src="https://tex.z-dn.net/?f=3%28-81%29%2B4y%5Ctextgreater9%20%5C%5C%20%5C%5C%20-243%2B4y%5Ctextgreater9%20%5C%5CPropiedad%20Conmutativa%3A%20%5C%5C%20%5C%5C%204y%5Ctextgreater9%2B243%20%5C%5C%20%5C%5C%204y%5Ctextgreater252%20%5C%5C%20%5C%5C%20y%5Ctextgreater%20%5Cboxed%7B%5Cdfrac%7B252%7D%7B4%7D%20%7D%20%5C%5C%20%5C%5C%20%5Cboxed%7By%5Ctextgreater63%7D" />

<img src="https://tex.z-dn.net/?f=%20%5Ccheckmark3x%2B4y%5C%20%5Ctextgreater%20%5C%209%5Chspace%7B4cm%7D%20%20%5Ccheckmark9x%2B12y%5C%20%5Ctextgreater%20%5C%20-27%5C%5C%203%28-81%29%2B4%2863%29%5C%20%5Ctextgreater%20%5C%209%5Chspace%7B3.4cm%7D9%28-81%29%2B12%2863%29%5C%20%5Ctextgreater%20%5C%20-27%20%5C%5C%20%20-243%2B252%5C%20%5Ctextgreater%20%5C%209%5Chspace%7B3.8cm%7D-729%2B756%5C%20%5Ctextgreater%20%5C%20-27%20%5C%5C%20%20%5C%5C%20%5Cboxed%7B9%5C%20%5Ctextgreater%20%5C%209%7D%5Chspace%7B5.4cm%7D%5Cboxed%7B27%5C%20%5Ctextgreater%20%5C%20-27%7D%20%5C%5C%20%20%5C%5C%20%24Podemos%20observar%20que%20en%20la%20ecuaci%5C%27on%20n%5C%27umero%20dos%20el%20lado%20izquierdo%20es%20%5C%5C%20%20mayor%20que%20el%20lado%20derecho%2C%20asi%20que%20es%20cierta%20la%20afirmaci%5C%27on." />

Saludos y Suerte!