Question

Sa se rezolve sistemele prin metoda substitutiei si a reducerii :

1•) {x+y=4
      {2x-y=-1

2•) {3x+2y=7
      {-x+4y=5

3•) {5x+y=4
      {3x-2y=5

Answer 1

$1)\left\{\begin{matrix} x + y = 4\\ 2x - y = - 1\end{matrix}\right.$

$x + 2x = 4 - 1$

$3x = 3$

$x = \frac{3}{3}$

$x = 1$

$x + y = 4$

$1 + y = 4$

$y = 4 - 1$

$y = 3$

$2)\left\{\begin{matrix} 3x + 2y = 7 \: | \times ( - 2)\\ - x + 4y = 5\end{matrix}\right.$

$\left\{\begin{matrix} - 6x - 4y = - 14\\ - x + 4y = 5\end{matrix}\right.$

$- 6x - x = - 14 + 5$

$- 7x = - 9 \: | \times ( - 1)$

$7x = 9$

$x = \frac{9}{7}$

$- x + 4y = 5$

$- \frac{9}{7} + 4y = 5 \: | \times 7$

$- 9 + 28y = 35$

$28y = 35 + 9$

$28y = 44$

$y = \frac{44}{28}$

$y = \frac{11}{7}$

$3)\left\{\begin{matrix} 5x + y = 4 \: | \times 2\\ 3x - 2y = 5\end{matrix}\right.$

$\left\{\begin{matrix} 10x + 2y = 8\\ 3x - 2y = 5\end{matrix}\right.$

$10x + 3x = 8 + 5$

$13x = 13$

$x = \frac{13}{13}$

$x = 1$

$3x - 2y = 5$

$3 \times 1 - 2y = 5$

$3 - 2y = 5$

$- 2y = 5 - 3$

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

$y = - 1$