Sistema de Equação
- Temos o seguinte sistema:
[tex]\large \boxed{\boxed{\left \{\sf {{3x-4y=1} \atop {x+3y=9}} \right. }}[/tex]
Resolvendo o sistema pela Regra de Cramer
- Tiramos os determinantes das variáveis
- Logo, fazemos a divisão dos Determinantes
Cálculo do sistema:
- Determinante das variáveis:
[tex]\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}}[/tex]
[tex]\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}}[/tex]
[tex]\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}}[/tex]
- Divisão dos Determinantes:
[tex]\large \boxed{\boxed{\sf \dfrac{D_{x}}{D} \Rightarrow \dfrac{39}{13} =3}}[/tex]
[tex]\large \boxed{\boxed{\sf \dfrac{D_{y}}{D} \Rightarrow \dfrac{26}{13} =2}}[/tex]
Resposta:
[tex]\huge \boxed{\boxed{ \sf S=\{3,2\}}}[/tex]
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