Metoda reducerii :
[tex]\left\{\begin{matrix}
3x + 2y = 7\\
- x + 4y = 5 \: | \times 3\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
3x + 2y = 7\\
- 3x + 12y = 15\end{matrix}\right.[/tex]
[tex]3x - 3x + 2y + 12y = 7 + 15[/tex]
[tex]14y = 22[/tex]
[tex]y = \frac{22}{14} [/tex]
[tex]y = \frac{11}{7} [/tex]
[tex] - x + 4y = 5[/tex]
[tex] - x + 4 \times \frac{11}{7} = 5 \: | \times 7[/tex]
[tex] - 7x + 44 = 35[/tex]
[tex] - 7x = 35 - 44[/tex]
[tex] - 7x = - 9 \: | \times ( - 1)[/tex]
[tex]7x = 9[/tex]
[tex]x = \frac{9}{7} [/tex]
[tex]S=\left\{(x,y)\right\}=\left\{(\frac{11}{7},\frac{9}{7})\right\}[/tex]
Metoda substituției :
[tex]\left\{\begin{matrix}
3x + 2y = 7\\
- x + 4y = 5\end{matrix}\right.[/tex]
[tex]3x + 2y = 7[/tex]
[tex]3x = 7 - 2y[/tex]
[tex]x = \frac{7 - 2y}{3} [/tex]
[tex] - x + 4y = 5[/tex]
[tex] - \frac{7 - 2y}{3} + 4y = 5 \: | \times 3[/tex]
[tex] - 7 + 2y + 12y = 15[/tex]
[tex]2y + 12y = 15 + 7[/tex]
[tex]14y = 22[/tex]
[tex]y = \frac{22}{14} [/tex]
[tex]y = \frac{11}{7} [/tex]
[tex]x = \frac{7 - 2y}{3} [/tex]
[tex]x = \frac{7 - 2 \times \frac{11}{7} }{3} [/tex]
[tex]x = \frac{7 - \frac{22}{7} }{3} [/tex]
[tex]x = \frac{ \frac{49 - 22}{7} }{3} [/tex]
[tex]x = \frac{ \frac{27}{7} }{3} [/tex]
[tex]x = \frac{27}{7} \times \frac{1}{3} [/tex]
[tex]x = \frac{27}{21} [/tex]
[tex]x = \frac{9}{7} [/tex]
[tex]S=\left\{(x,y)\right\}=\left\{(\frac{11}{7},\frac{9}{7})\right\}[/tex]
