Question

Sistem
{-4x+5y=17
{x-y=2

Answer 1

1)Metoda reducerii :

$\left\{\begin{matrix}</p><p> - 4x + 5y = 17\\ x - y = 2 \: | \times 4</p><p></p><p>\end{matrix}\right.$

$\left\{\begin{matrix}</p><p> - 4x + 5y = 17\\ </p><p></p><p>4x - 4y = 8\end{matrix}\right.$

$- 4x + 4x + 5y - 4y = 17 + 8$

$y = 25$

$x - y = 2$

$x - 25 = 2$

$x = 2 + 25$

$x = 27$

$S=\left\{(x,y)\right\}=\left\{(27,25)\right\}$

Metoda substituției :

$\left\{\begin{matrix}</p><p> - 4x + 5y = 17\\ </p><p></p><p>x - y = 2\end{matrix}\right.$

$x - y = 2 = > x = 2 + y$

$- 4x + 5y = 17$

$- 4(2 + y) + 5y = 17$

$- 8 - 4y + 5y = 17$

$- 4y + 5y = 17 + 8$

$y = 25$

$x = 2 + y = 2 + 25 = 27$

$S=\left\{(x,y)\right\}=\left\{(27,25)\right\}$

Answer 2

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