Question

Usando a regra de Cramer resolva os sistemas.

Answer 1

Explicação passo-a-passo:

a)

$D=\left[\begin{array}{ccc}2&3\\3&2\\\end{array}\right]$

$detD=2.2-3.3=4-9=-5$

$D_{x}=\left[\begin{array}{ccc}14&3\\16&2\\\end{array}\right]$

$detD_{x}=14.2-3.16=28-48=-20$

$D_{y} =\left[\begin{array}{ccc}2&14\\3&16\\\end{array}\right]$

$detD_{y} =2.16-14.3=32-42=-10$

$x=\frac{detD_{x} }{detD} =\frac{-20}{-5}=4\\ \\y=\frac{detD_{y} }{detD} =\frac{-10}{-5}=2$

b)

$D=\left[\begin{array}{ccc}1&-3\\2&1\\\end{array}\right]$

$detD=1.1-(-3).2=1+6=7$

$D_{x}=\left[\begin{array}{ccc}2&-3\\11&1\\\end{array}\right]$

$detD_{x} =2.1-(-3).11=2+33=35$

$D_{y} =\left[\begin{array}{ccc}1&2\\2&11\\\end{array}\right]$

$detD_{y} =1.11-2.2=11-4=7$

$x=\frac{detD_{x} }{detD} =\frac{35}{7}=5\\ \\y=\frac{detD_{y} }{detD} =\frac{7}{7}=1$