Question

{3x+4y=13 {2x+5y=11

pfvr me ajudemmmm

Answer 1

Sistema de Equação

• Temos o Seguinte Sistema:

$\large \boxed{ \begin{array}{lr}\boxed{ \begin{array}{lr} \\ \begin{cases} \sf3x + 4y = 13 \\ \\ \sf2x + 5y = 11 \end{cases} \\ \: \end{array}}\end{array}}$

Para resolver Essa sistema, vou utilizar 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:

$\begin{gathered}\boxed{\begin{array}{lr} \\\large \sf D=\left[\begin{array}{ccc}\sf3&\sf4\\\sf2&\sf5\\\end{array}\right] \\\\\\\large \sf D=15-( + 8)\\\\\large \sf D=15 - 8\\\\\large \sf D=7\\ \:\end{array}}\end{gathered}$

Determinante do x:

$\begin{gathered}\boxed{\begin{array}{lr} \\\large \sf D_{x}=\left[\begin{array}{ccc}\sf13&\sf4\\\sf11&\sf5\\\end{array}\right] \\\\\\\large \sf D_{x}=65-( +44)\\\\\large \sf D_{x}=65 - 44\\\\\large \sf D_{x}=21 \\ \:\end{array}}\end{gathered}$

Determinante do y:

$\begin{gathered}\boxed{\begin{array}{lr} \\\large \sf D_{y}=\left[\begin{array}{ccc}\sf3&\sf13\\\sf2&\sf11\\\end{array}\right] \\\\\\\large \sf D_{y}=33-(+26)\\\\\large \sf D_{y}=33 - 26\\\\\large \sf D_{y}=7\\ \:\end{array}}\end{gathered}$

Divisão dos Determinantes:

$\large \boxed{\boxed{\sf \dfrac{D_{x}}{D} \Rightarrow \dfrac{21}{7} =3}} \\ \\ \large \boxed{\boxed{\sf \dfrac{D_{y}}{D}\Rightarrow \dfrac{7}{7} =1}}$

➡️ Resposta:

$\huge \boxed{\boxed{ \sf S=\{3,1\}}}$

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