Question

Resolva os sistema usando a regra de Cramer.

{ x + y = 3
{ 2x - 3y = - 4

Answer 1

Resposta:

x=1 e y=2

Explicação passo a passo:

Regra de Cramer

$\displaystyle\\\left[\begin{array}{ccc}1&1\\2&-3\end{array}\right] \dot\\\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}3\\-4\end{array}\right] \\\\\\\Delta =\left[\begin{array}{ccc}1&1\\2&-3\end{array}\right] =-3-2=-5$

$\displaystylex=\frac{\Delta x}{\Delta } =\frac{\left[\begin{array}{ccc}3&1\\-4&-3\end{array}\right] }{\Delta} =\frac{-9+4}{-5}= \frac{-5}{-5} =1\\\\\\y=\frac{\Delta y}{\Delta } =\frac{\left[\begin{array}{ccc}1&3\\2&-4\end{array}\right] }{\Delta} =\frac{-4-6}{-5}= \frac{-10}{-5} =2$