Question

Sistema lineares.

3x-y=5
-2x-2y=-22

Answer 1

Olá,

acha delta..

$\Delta= \left|\begin{array}{ccc}3&-1\\-2&-2\\\end{array}\right|\\\\ \Delta=3\cdot(-2)-(-1)\cdot(-2)\\ \Delta=-6+1\cdot(-2)\\ \Delta=-6-2\\ \Delta=-8$

acha delta x..

$\Delta_x= \left|\begin{array}{ccc}5&-1\\-22&-2\\\end{array}\right|\\\\ \Delta_x=5\cdot(-2)-(-1)\cdot(-22)\\ \Delta_x=-10-22\\ \Delta_x=-32$

acha delta y..

$\Delta_y= \left|\begin{array}{ccc}3&5\\-2&-22\\\end{array}\right|\\\\ \Delta_y=3\cdot(-22)-5\cdot(-2)\\ \Delta_y=-66+10\\ \Delta_y=-56$

Agora divide os determinantes x e y, pelo determinante delta..

$x= \dfrac{\Delta_x}{\Delta}= \dfrac{-32}{-8}=4\\\\\\ y= \dfrac{\Delta_y}{\Delta}= \dfrac{-56}{-8} =7$

Então a solução do sistema será..

$\Large\boxed{S=\{(4,7)\}}$