Question

Rezolvati sistemul de ecuatii
-2x+3y=11
7x+y=-4
DAU COROANA

Answer 1

Metoda reduceri
-2x+3y=11 l×7
7x+y=-4     l×2
-14x+21y=77
+14x+2y= - 8
--------------------  +
 /     23y=69   ⇒  y=69/23  ⇒  y = 3

-2x+3y=11  
7x+y=-4   l×( - 3)

  -2x+3y=11
-21x-3y=12
-------------------   +
- 23x  / =23  ⇒    x= -1

S={ ( -1; 3) }

Answer 2

I) Metoda reducerii :
$\left\{\begin{matrix} - 2x + 3y = 11\\ 7x + y = - 4 \: | \times ( - 3)\end{matrix}\right.$

$\left\{\begin{matrix} - 2x + 3y = 11\\ - 21x - 3y = 12\end{matrix}\right.$

$- 2x - 21x + 3y - 3y = 11 + 12$

$- 23x = 23 \: | \div ( - 23)$

$x = - 1$

$- 2x + 3y = 11$

$- 2 \times ( - 1) + 3y = 11$

$2 + 3y = 11$

$3y = 11 - 2$

$3y = 9 \: | \div 3$

$y = 3$

II) Metoda substituției :

$\left\{\begin{matrix} - 2x + 3y = 11\\ 7x + y = - 4\end{matrix}\right.$

$- 2x + 3y = 11$

$x = - \frac{11 - 3y}{2}$

$x = \frac{ 3y - 11}{2}$

$7x + y = - 4$

$7 \times \frac{3y - 11}{2} + y = - 4$

$\frac{21y - 77}{2} + y = - 4 \: | \times 2$

$21y - 77 + 2y = - 8$

$21y + 2y = - 8 + 77$

$23y = 69 \: | \div 23$

$y = 3$

$7x + y = - 4$

$7x + 3 = - 4$

$7x = - 4 - 3$

$7x = - 7 \: | \div 7$

$x = - 1$

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

$S=\left \{(-1 , 3)\right \}$