Question

Resolva o sistema a seguir usando determinantes.
4x - y = 8
2x + 2y = 3

Answer 1

Explicação passo-a-passo:

$\sf \begin{cases} \sf 4x-y=8 \\ \sf 2x+2y=3 \end{cases}$

$\sf D=\left(\begin{array}{cc} \sf 4 & \sf -1 \\ \sf 2 & \sf 2 \end{array}\right)$

$\sf det~(D)=4\cdot2-2\cdot(-1)$

$\sf det~(D)=8+2$

$\sf det~(D)=10$

$\sf D_x=\left(\begin{array}{cc} \sf 8 & \sf -1 \\ \sf 3 & \sf 2 \end{array}\right)$

$\sf det~(D_x)=8\cdot2-3\cdot(-1)$

$\sf det~(D_x)=16+3$

$\sf det~(D_x)=19$

$\sf D_y=\left(\begin{array}{cc} \sf 4 & \sf 8 \\ \sf 2 & \sf 3 \end{array}\right)$

$\sf det~(D_y)=4\cdot3-2\cdot8$

$\sf det~(D_y)=12-16$

$\sf det~(D_y)=-4$

Assim:

$\sf x=\dfrac{det~(D_x)}{det~(D)}~\Rightarrow~\red{x=\dfrac{19}{10}}$

$\sf y=\dfrac{det~(D_y)}{det~(D)}~\Rightarrow~\red{y=\dfrac{-4}{10}}$