Question

rezolvati sistemul de ecuatii:
$1.8 \times x + 6 \times y = 51 \\ x + y = 12$

Answer 1

I) Metoda reducerii :

$\left\{\begin{matrix} 1.8x + 6y = 51\\ x + y = 12 \: | \times ( - 6)\end{matrix}\right.$

$\left\{\begin{matrix} 1.8x + 6y = 51\\ - 6x - 6y = - 72\end{matrix}\right.$

$1.8x - 6x + 6y - 6y = 51 - 72$

$1.8x - 6x = 51 - 72$

$- 4.2x = - 21 \: | \times ( - 1)$

$4.2x = 21$

$x = \frac{21}{4.2}$

$x = 5$

$x + y = 12$

$5 + y = 12$

$y = 12 - 5$

$y = 7$

II) Metoda substituției :

$\left\{\begin{matrix} 1.8x + 6y = 51\\ x + y = 12\end{matrix}\right.$

$1.8x + 6y = 51$

$y = \frac{51 - 1.8x}{6}$

$x + y = 12$

$x + \frac{51 - 1.8x}{6} = 12 \: | \times 6$

$6x + 51 - 1.8x = 72$

$6x - 1.8x = 72 - 51$

$4.2x = 21$

$x = \frac{21}{4.2}$

$x = 5$

$y = \frac{51 - 1.8x}{6}$

$y = \frac{51 - 1.8 \times 5}{6}$

$y = \frac{51 - 9}{6}$

$y = \frac{42}{6}$

$y = 7$