Question

a solução do sistema linear é
{3x-4y=1
{x+3y=9​

Answer 1

Sistema de Equação

• Temos o seguinte sistema:

$\large \boxed{\boxed{\left \{\sf {{3x-4y=1} \atop {x+3y=9}} \right. }}$

Resolvendo o sistema pela Regra de Cramer

• Tiramos os determinantes das variáveis

• Determinante do x

• Determinante do y

• Logo, fazemos a divisão dos Determinantes

Cálculo do sistema:

• Determinante das variáveis:

$\boxed{\begin{array}{lr} \\\large \sf D=\left[\begin{array}{ccc}\sf3&\sf-4\\\sf1&\sf3\\\end{array}\right] \\\\\\\large \sf D=9-( -4)\\\\\large \sf D=9+4\\\\\large \sf D=13 \\ \:\end{array}}$

• Determinante do x:

$\boxed{\begin{array}{lr} \\\large \sf D_{x}=\left[\begin{array}{ccc}\sf1&\sf-4\\\sf9&\sf3\\\end{array}\right] \\\\\\\large \sf D_{x}=3-(-36)\\\\\large \sf D_{x}=36+3\\\\\large \sf D_{x}=39 \\ \:\end{array}}$

• Determinante do y:

$\boxed{\begin{array}{lr} \\\large \sf D_{y}=\left[\begin{array}{ccc}\sf3&\sf1\\\sf1&\sf9\\\end{array}\right] \\\\\\\large \sf D_{y}=27-(+1)\\\\\large \sf D_{y}=27-1'\\\\\large \sf D_{y}=26 \\ \:\end{array}}$

• Divisão dos Determinantes:

$\large \boxed{\boxed{\sf \dfrac{D_{x}}{D} \Rightarrow \dfrac{39}{13} =3}}$

$\large \boxed{\boxed{\sf \dfrac{D_{y}}{D} \Rightarrow \dfrac{26}{13} =2}}$

Resposta:

$\huge \boxed{\boxed{ \sf S=\{3,2\}}}$

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