Question

ME AJUDEM POR FAVOR, 30 PONTOS

Calcule o valor de x e y, nos sistemas a seguir usando a regra de Cramer

a) x = 11 -y
x - y =3


b) 4x - y = 2
2y = 7 - 3x

c) 3x = 7 - 5y
2x = 11+ 3y

Answer 1

calcule o determinante e depois os respectivos determinantes de x e y substituindo os valores e depois use a formula x=Dx/D

Answer 2

a) $D=\left[\begin{array}{cc}1&1\\1&-1\end{array}\right]=-1-1=-2$

$D_x=\left[\begin{array}{cc}11&1\\3&-1\end{array}\right]=-11-3=-14$

$D_y=\left[\begin{array}{cc}1&11\\1&3\end{array}\right]=3-11=-8$

$x=\frac{D_x}{D}=\frac{-14}{-2}  =7$

$y=\frac{D_y}{D}=\frac{-8}{-2}=4$

b) $D=\left[\begin{array}{cc}4&-1\\3&2\end{array}\right]=8-(-3)=8+3=11$

$D_x=\left[\begin{array}{cc}2&-1\\7&2\end{array}\right]=4-(-7)=4+7=11$

$D_y=\left[\begin{array}{cc}4&2\\3&7\end{array}\right]=28-6=22$

$x=\frac{D_x}{D}=\frac{11}{11}=1$

$y=\frac{Dy}{D}=\frac{22}{11}=2$

c) $D=\left[\begin{array}{cc}3&5\\2&-3\end{array}\right]=-9-10=-19$

$D_x=\left[\begin{array}{cc}7&5\\11&-3\end{array}\right]=-21-55=-76$

$D_y=\left[\begin{array}{cc}3&7\\2&11\end{array}\right]=33-14=19$

$x=\frac{D_x}{D}=\frac{-76}{-19}  =4$

$y=\frac{D_y}{D}=\frac{19}{-19}=-1$