Question

Rezolvați sistemul prin metoda reducerii și metoda substituției. AJUTO VA ROG!! ​

Answer 1

Metoda reducerii :

$\left\{\begin{matrix}</p><p>3x + 2y = 7\\ </p><p></p><p> - x + 4y = 5 \: | \times 3\end{matrix}\right.$

$\left\{\begin{matrix}</p><p>3x + 2y = 7\\ </p><p></p><p> - 3x + 12y = 15\end{matrix}\right.$

$3x - 3x + 2y + 12y = 7 + 15$

$14y = 22$

$y = \frac{22}{14}$

$y = \frac{11}{7}$

$- x + 4y = 5$

$- x + 4 \times \frac{11}{7} = 5 \: | \times 7$

$- 7x + 44 = 35$

$- 7x = 35 - 44$

$- 7x = - 9 \: | \times ( - 1)$

$7x = 9$

$x = \frac{9}{7}$

$S=\left\{(x,y)\right\}=\left\{(\frac{11}{7},\frac{9}{7})\right\}$

Metoda substituției :

$\left\{\begin{matrix}</p><p>3x + 2y = 7\\ </p><p></p><p> - x + 4y = 5\end{matrix}\right.$

$3x + 2y = 7$

$3x = 7 - 2y$

$x = \frac{7 - 2y}{3}$

$- x + 4y = 5$

$- \frac{7 - 2y}{3} + 4y = 5 \: | \times 3$

$- 7 + 2y + 12y = 15$

$2y + 12y = 15 + 7$

$14y = 22$

$y = \frac{22}{14}$

$y = \frac{11}{7}$

$x = \frac{7 - 2y}{3}$

$x = \frac{7 - 2 \times \frac{11}{7} }{3}$

$x = \frac{7 - \frac{22}{7} }{3}$

$x = \frac{ \frac{49 - 22}{7} }{3}$

$x = \frac{ \frac{27}{7} }{3}$

$x = \frac{27}{7} \times \frac{1}{3}$

$x = \frac{27}{21}$

$x = \frac{9}{7}$

$S=\left\{(x,y)\right\}=\left\{(\frac{11}{7},\frac{9}{7})\right\}$