Question

Rezolvati sistemul prin metoda substitutiei:
2(x+3)-3y=2
{
5x-3(2y-1)=-4
Vreau rezolvarea, nu numai rezultatul!

Answer 1

$\left\{\begin{matrix}</p><p>2(x + 3) - 3y = 2 \\ </p><p> 5x - 3(2y - 1) = - 4\end{matrix}\right$

$\left\{\begin{matrix}</p><p>2 \times x + 2 \times 3 - 3y = 2\\ </p><p></p><p>5x - 3 \times 2y - 3 \times ( - 1) = - 4\end{matrix}\right$

$\left\{\begin{matrix}</p><p>2x + 6 - 3y = 2\\ </p><p></p><p>5x - 6y + 3 = - 4\end{matrix}\right$

$\left\{\begin{matrix}</p><p>2x - 3y = 2 - 6\\ </p><p>5x - 6y = - 4 - 3</p><p>\end{matrix}\right$

$\left\{\begin{matrix}</p><p>2x - 3y = - 4\\ </p><p></p><p>5x - 6y = - 7\end{matrix}\right$

$2x - 3y = - 4$

$2x = - 4 + 3y$

$x = \frac{ - 4 + 3y}{2}$

$5x - 6y = - 7$

$5 \times \frac{ - 4 + 3y}{2} - 6y = - 7$

$\frac{5( - 4 + 3y)}{2} - 6y = - 7$

$\frac{5 \times ( - 4) + 5 \times 3y}{2} - 6y = - 7$

$\frac{ - 20 + 15y}{2} - 6y = - 7 \: | \times 2$

$- 20 + 15y - 12y = - 14$

$15y - 12y = - 14 + 20$

$3y = 6 \: | \div 3$

$y = 2$

$x = \frac{ - 4 + 3y}{2}$

$x = \frac{ - 4 + 3 \times 2}{2}$

$x = \frac{ - 4 + 6}{2}$

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

$x = 1$