Question

rezolvati sistemele
a) x+y=10
x-y=2

b) 3x+1=y+6
4x-5y=8
 dau coroana! va rog ajutati-ma

Answer 1

a) y |-----| x+y=10
x |-----|--|
2 Egalam partile

1. Care va fi suma dupa egalare?
10-2=8

2. Cat este y?
8:2=4

3. Cat este x?
4+2=6

Answer 2

a)I) Metoda reducerii :

$\left\{\begin{matrix} x + y = 10\\ x - y = 2\end{matrix}\right.$

$x + x + y - y = 10 + 2$

$2x = 12 \: | \div 2$

$x = 6$

$x + y = 10$

$6 + y = 10$

$y = 10 - 6$

$y = 4$

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

$S=\left \{ (6,4) \right \}$

II) Metoda substituției :

$\left\{\begin{matrix} x + y = 10\\ x - y = 2\end{matrix}\right.$

$x + y = 10$

$x = 10 - y$

$x - y = 2$

$10 - y - y = 2$

$- y - y = 2 - 10$

$- 2y = - 8 \: | \div ( - 2)$

$y = 4$

$x = 10 - y$

$x = 10 - 4$

$x = 6$

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

$S=\left \{ (6,4) \right \}$

b)I) Metoda reducerii :

$\left\{\begin{matrix} 3x + 1 = y + 6\\ 4x - 5y = 8\end{matrix}\right.$

$\left\{\begin{matrix} 3x - y = 6 - 1\\ 4x - 5y = 8\end{matrix}\right.$

$\left\{\begin{matrix} 3x - y = 5 \: | \times ( - 5)\\ 4x - 5y = 8\end{matrix}\right.$

$\left\{\begin{matrix} - 15x + 5y = - 25\\ 4x - 5y = 8\end{matrix}\right.$

$- 15x + 4x + 5y - 5y = - 25 + 8$

$- 11x = - 17 \: | \times ( - 1)$

$11x = 17$

$x = \frac{17}{11}$

$3x - y = 5$

$3 \times \frac{17}{11} - y = 5$

$\frac{51}{11} - y = 5 \: | \times 11$

$51 - 11y = 55$

$- 11y = 55 - 51$

$- 11y = 4 \: | \times ( - 1)$

$11y = - 4$

$y = - \frac{4}{11}$

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

$S=\left \{ ( \frac{17}{11} , - \frac{4}{11} ) \right \}$

II) Metoda substituției :

$\left\{\begin{matrix} 3x - y = 5\\ 4x - 5y = 8\end{matrix}\right.$

$3x - y = 5$

$- y = 5 - 3x \: | \times ( - 1)$

$y = 3x - 5$

$4x - 5y = 8$

$4x - 5(3x - 5) = 8$

$4x - 15x + 25 = 8$

$4x - 15x = 8 - 25$

$- 11x = - 17 \: | \times ( - 1)$

$11x = 17$

$x = \frac{17}{11}$

$y = 3x - 5$

$y = 3 \times \frac{17}{11} - 5$

$y = \frac{51}{11} - 5$

$y = \frac{51}{11} - \frac{55}{11}$

$y = \frac{51 - 55}{11}$

$y = - \frac{4}{11}$

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

$S=\left \{ ( \frac{17}{11} , - \frac{4}{11} ) \right \}$