Question

imi poate explica si mie cineva cum se fac astea?

Answer 1

   
-2x + y = +2
 3x + y = -1

Sistem de 2 ecuatii si 2 necunoscute.
Pentru rezolvare se poate folosi metoda substitutiei sau metoda reducerii.

[tex]\displaystyle\\ \text{Metoda substitutiei:}\\\\ \begin{cases} -2x + y = +2~~~~~\Longrightarrow~~\boxed{\bf y=2x+2}~~\text{\bf substitutie} \\ 3x + y = -1\\ \end{cases}\\\\ \text{Inlocuim pe y in a 2-a ecuatie. }\\\\ 3x + 2x+2 = -1\\ 3x + 2x = -1-2\\ 5x=-3\\\\ \boxed{\bf x= -\frac{3}{5}} \\\\ \text{Ne intoarcem la substitutie pentru a-l afla pe y.}\\ y=2x+2\\\\ y=2\cdot \frac{-3}{5}+2 = \frac{2(-3)}{5}+\frac{10}{5} =\frac{-6}{5}+\frac{10}{5} = \frac{10-6}{5} \\\\ \boxed{\bf y=\frac{4}{5}}[/tex]


[tex]\displaystyle\\ \text{Metoda reducerii:}\\\\ \begin{cases} -2x + y = +2~~~~\Big| \cdot 3\\ 3x + y = -1~~~~~\Big| \cdot 2\\ \end{cases}\\\\ \text{Inmultim ecuatia 1 cu 3 si ecuatia 2 cu 2. }\\\\ \begin{cases} -6x + 3y = 6\\ ~~6x + 2y = -2\\ \end{cases}\\ \text{-----------------------Adunam ecuatiile si se va reduce necunoscuta x.}\\ ~~~~~~/ ~~~~5y = 4\\\\ \boxed{\bf y = \frac{4}{5} }[/tex]

[tex]\displaystyle\\ \text{Rescriem una din ecuatii.}\\ 3x + y = -1\\ x = \frac{-y-1}{3}=-\frac{y+1}{3}=-\frac{\dfrac{4}{5} +1}{3}-\frac{\dfrac{9}{5}}{3}=- \frac{9}{15} \\\\ \boxed{\bf x = - \frac{3}{5}}[/tex]