Question

Utilizando a regra de cramer determine a solução do sistema linear a segui.
{ 2x + 8y = 0
{ 9x + 6y = 15

Answer 1

D = 2*6 – 8*9 →12 – 72 → – 60 
D ≠ 0

solução do sistema:

x = Dx/D e y = Dy / D 

Dx:
  0         8 
15        6 

0*6 – 8*15 = – 120 

x = Dx / D = – 120/– 60 = 2 

Dy:

2      0 
9     15 

2*15 – 0*9 = 30 

y = Dy / D = 30 / – 60 = – 0,5 

Answer 2

$\left \{ {{2x+8y=0} \atop {9x+6y=15}} \right.$ 

vamos calcular o determinante

$D= \left[\begin{array}{ccc}2&8\\9&6\\\end{array}\right] =12-(72)=12-72=-60 \\ \\ \\ D_X= \left[\begin{array}{ccc}0&8\\15&6\\\end{array}\right] =0-120=-120 \\ \\ \\ D_Y= \left[\begin{array}{ccc}2&0\\9&15\\\end{array}\right] =30-0=30 \\ \\ \\ x= \frac{D_X}{D} = \frac{-120}{-60} =2 \\ \\ y= \frac{D_Y}{D} = \frac{30}{-60} =- \frac{1}{2} \\ \\ S=\{- \frac{1}{2} ,2\}$