Question

"rezolvați sistemul de ecuatii" 2x+3y=10 3x-y=4

Answer 1

I) Metoda reducerii :

$\left\{\begin{matrix} 2x + 3y = 10\\ 3x - y = 4 \: | \times 3\end{matrix}\right.$

$\left\{\begin{matrix} 2x + 3y = 10\\ 9x - 3y = 12\end{matrix}\right.$

$2x + 9x + 3y - 3y = 10 + 12$

$11x = 22 \: | \div 11$

$x = 2$

$3x - y = 4$

$3 \times 2 - y = 4$

$6 - y = 4$

$- y = 4 - 6$

$- y = - 2 \: | \times ( - 1)$

$y = 2$

II) Metoda substituției :

$\left\{\begin{matrix} 2x + 3y = 10\\ 3x - y = 4\end{matrix}\right.$

$2x + 3y = 10$

$x = \frac{10 - 3y}{2}$

$3x - y = 4$

$3 \times \frac{10 - 3y}{2} - y = 4$

$\frac{30 - 9y}{2} - y = 4 \: | \times 2$

$30 - 9y - 2y = 8$

$- 9y - 2y = 8 - 30$

$- 11y = - 22 \: | \div ( - 11)$

$y = 2$

$x = \frac{10 - 3y}{2}$

$x = \frac{10 - 3 \times 2}{2}$

$x = \frac{10 - 6}{2}$

$x = \frac{4}{2}$

$x = 2$