Question

regra de cramer : {x+y=1 {2x+y=4

Answer 1

$\begin{cases}x+y=1\\ 2x+y=4\end{cases}\\\\\\\\ D= \left[\begin{array}{cc}1&1\\2&1\end{array}\right] \\\\ D=\{1.1\}-\{2.1\}\to~~ D = 1-2\to~~\boxed{D = -1}$


$D_x= \left[\begin{array}{cc}1&1\\4&1\end{array}\right] \\\\ D_x=\{1.1\}-\{4.1\}\to~~ D_x = 1-4\to~~\boxed{D_x = -3}\\\\\\\\ D_y= \left[\begin{array}{cc}1&1\\2&4\end{array}\right] \\\\ D_y=\{1.4\}-\{2.1\}\to~~ D_y = 4-2\to~~\boxed{D_y = 2}$


$x= \dfrac{D_x}{D} \to~~ x= \dfrac{-3}{-1} \to~~ \boxed{x=3}\\\\\\y= \dfrac{D_y}{D} \to~~ y= \dfrac{2}{-1} \to~~ \boxed{y=-2}\\\\\\\\\\ \large\boxed{\boxed{S=\{3~;~-2\}}}$