Question

Rezolvati, in multimea numerelor reale, sistemul de ecuatii: 3x + y = -2 , -5x-3y= 2

Answer 1

I) Metoda substituției :

$\left\{\begin{matrix} 3x + y = - 2\\ - 5x - 3y = 2\end{matrix}\right.$

$3x + y = - 2$

$y = - 2 - 3x$

$- 5x - 3y = 2$

$- 5x - 3( - 2 - 3x) = 2$

$- 5x + 6 + 9x = 2$

$- 5x + 9x = 2 - 6$

$4x = - 4 \: | \div 4$

$x = - 1$

$y = - 2 - 3x$

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

$y = - 2 + 3$

$y = 1$

II) Metoda reducerii :

$\left\{\begin{matrix} 3x + y = - 2 \: | \times 3\\ - 5x - 3y = 2\end{matrix}\right.$

$\left\{\begin{matrix} 9x + 3y = - 6\\ - 5x - 3y = 2\end{matrix}\right.$

$9x - 5x + 3y - 3y = - 6 + 2$

$4x = - 4 \: | \div 4$

$x = - 1$

$3x + y = - 2$

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

$- 3 + y = - 2$

$y = - 2 + 3$

$y = 1$