1)Metoda reducerii :
[tex]\left\{\begin{matrix}
- 4x + 5y = 17\\ x - y = 2 \: | \times 4
\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
- 4x + 5y = 17\\
4x - 4y = 8\end{matrix}\right.[/tex]
[tex] - 4x + 4x + 5y - 4y = 17 + 8[/tex]
[tex]y = 25[/tex]
[tex]x - y = 2[/tex]
[tex]x - 25 = 2[/tex]
[tex]x = 2 + 25[/tex]
[tex]x = 27[/tex]
[tex]S=\left\{(x,y)\right\}=\left\{(27,25)\right\}[/tex]
Metoda substituției :
[tex]\left\{\begin{matrix}
- 4x + 5y = 17\\
x - y = 2\end{matrix}\right.[/tex]
[tex]x - y = 2 = > x = 2 + y[/tex]
[tex] - 4x + 5y = 17[/tex]
[tex] - 4(2 + y) + 5y = 17[/tex]
[tex] - 8 - 4y + 5y = 17[/tex]
[tex] - 4y + 5y = 17 + 8[/tex]
[tex]y = 25[/tex]
[tex]x = 2 + y = 2 + 25 = 27[/tex]
[tex]S=\left\{(x,y)\right\}=\left\{(27,25)\right\}[/tex]
