2 numeros que multiplicados entre ellos me de - 14 y al sumarlos me den - 5?

Lo expresamos así :

Dos números que multiplicados entre ellos me den 14 : <img src="https://tex.z-dn.net/?f=x%20%5Ctimes%20y%3D%20-14" />

Al sumarlos den - 5 : <img src="https://tex.z-dn.net/?f=x%2By%3D%20-5" />

Resolvemos por el Método de Sustitución :

<img src="https://tex.z-dn.net/?f=x%20%5Ctimes%20y%3D%20-14%5Ccheckmark%20%5C%5C%20%24Despejamos%20a%20%5Ctextbf%7Bx%7D%3B%20Tendremos%20que%20pasar%20a%20%5Ctextbf%7Bdividir%7D%20a%20%5Ctextbf%7By%7D%2C%20a%20la%20parte%20%5C%5C%20%5Ctextbf%7Bderecha%7D%3A%20%5C%5C%20%5C%5C%20%5Cboxed%7B%5Cboxed%7B%5Ctextbf%7Bx%3D%7D%20-%5Cdfrac%7B%5Ctextbf%7B14%7D%7D%7B%5Ctextbf%7By%7D%20%7D%7D%7D%5Ccheckmark%20%5Ccheckmark%20%5C%5C%20%5C%5C%20Sustituimos%20este%20valor%2C%20en%20la%20otra%20ecuaci%5C%27on%3A%20%5C%5C%20%5C%5C%20x%2By%3D%20-5%20%5C%5C%20%5C%5C%20-%5Cdfrac%7B%5Ctextbf%7B14%7D%7D%7B%5Ctextbf%7By%7D%20%7D%7D%2By%3D%20-5%20%5C%5C%20%5C%5C%20%24Tenemos%20que%20encontrar%20el%20%5Ctextbf%7BM%5C%27inimo%20Com%5C%27un%20M%5C%27ultiplo%7D%20de%20los%20%5C%5C%20Denominadores%20de%20cada%20fracci%5C%27on%3A%20%5C%5C%20%5C%5C%20MCM%3D%20%5Cboxed%7B%5Ctextbf%7By%7D%7D" />

<img src="https://tex.z-dn.net/?f=%7B%24Tenemos%20que%20Multiplicar%20al%20MCM%2C%20por%20cada%20miembro%20de%20la%20ecuaci%5C%27on%3A%20%5C%5C%20%5C%5C%20-%20%28%5Cnot%7By%7D%29%5Cdfrac%7B%5Ctextbf%7B14%7D%7D%7B%20%5Cnot%7By%7D%7D%20%7D%7D%2B%28y%29y%3D%20-5%28y%29%20%5C%5C%20%5C%5C%20%28-14%29%2B%20y%5E%7B2%7D%20%3D%20-5y%20%5C%5C%20%24Ordenamos%20los%20T%5C%27erminos%3A%20%5C%5C%20%5C%5C%20y%5E%7B2%7D%2B5y-14%3D%200%20%5C%5C%20%24Tendremos%20que%20buscar%20dos%20numeros%20que%20multiplicados%20den%20-14%2C%20y%20que%20%5C%5C%20sumados%20den%205%3A%20%5C%5C%20%5C%5C%20%5Cboxed%7B%5Cboxed%7B%5Ctextbf%7B%287%3B-2%29%7D%7D%7D%20%5C%5C%20%5C%5C%20%28y%2B7%29%20%28y-2%29%3D%200%20%5C%5C%20%5C%5C%20%28y%2B7%29%3D%200%20%5Ctimes%20%28y-2%29%20%5C%5C%20%5C%5C%20y%2B7%3D%200%20%5C%5C%20%5C%5C%5Cboxed%7B%5Cboxed%7B%5Ctextbf%7B%20y%7D_%7B%5Ctextbf%7B%201%7D%7D%20%5Ctextbf%7B%20%3D%20-7%7D%7D%7D%5Ccheckmark%20%5Ccheckmark" />

<img src="https://tex.z-dn.net/?f=%28y%2B7%29%20%28y-2%29%3D%200%20%5C%5C%20%5C%5C%20%28y-2%29%3D%200%20%5Ctimes%20%28y%2B7%29%20%5C%5C%20%5C%5C%20y-2%3D%200%20%5C%5C%20%5C%5C%5Cboxed%7B%5Cboxed%7B%5Ctextbf%7B%20y%7D_%7B%5Ctextbf%7B%202%7D%7D%20%5Ctextbf%7B%20%3D2%7D%7D%7D%5Ccheckmark%20%5Ccheckmark%20%5C%5C%20%5C%5C%20%24Por%20lo%20tanto%3A%20%5C%5C%20%5C%5C%20%5Cboxed%7B%5Cboxed%7B%5Ctextbf%7B%20x%3D%20-7%20%7D%7D%7D%5C%5C%20%5Cboxed%7B%5Cboxed%7B%5Ctextbf%7B%20y%3D%202%7D%7D%7D" />

Comprobación :

Sustituimos valores :

<img src="https://tex.z-dn.net/?f=x%20%5Ctimes%20y%3D%20-14%20%5C%5C%20-7%20%5Ctimes%202%3D%20-14%20%5C%5C%20%20%5C%5C%20%5Cboxed%7B%5Cboxed%7B%5Ctextbf%7B-14%3D%20-14%7D%7D%7D%20%5C%5C%20%20%5C%5C%20x%2By%3D%20-5%20%5C%5C%20%20%5C%5C%20-7%2B2%3D%20-5%20%5C%5C%20%20%5C%5C%20%5Cboxed%7B%5Cboxed%7B%5Ctextbf%7B-5%3D%20-5%7D%7D%7D" />

Saludos y Suerte!