Question

Resolva as questões usando a regra de clamer,

Answer 1

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===========================================================$\tt{a)}~\begin{cases}\sf{3x-4y=11}\\\sf{x+y=6}\end{cases}\\\tt{A}=\begin{vmatrix}\sf{3}&\sf{-4}\\\sf{1}&\sf{1}\end{vmatrix}\\\sf{det~A=3+4=7}\\\tt{A_x}=\begin{vmatrix}\sf{11}&\sf{-4}\\\sf{6}&\sf{1}\end{vmatrix}\\\sf{det~A_x=11+24=35}\\\sf{A_y}=\begin{vmatrix}\sf{3}&\sf{11}\\\sf{1}&\sf{6}\end{vmatrix}\\\sf{det~A_y=18-11=7}\\\sf{x=\dfrac{det~A_x}{det~A}=\dfrac{35}{7}=5}\\\sf{y=\dfrac{det~A_y}{det~A}=\dfrac{7}{7}=1}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{s=\{5,1\}}}}}}$

$\tt{b)}~\begin{cases}\sf{4x-y=6}\\\sf{x+2y=15}\end{cases}\\\sf{P}=\begin{vmatrix}\sf{4}&\sf{-1}\\\sf{1}&\sf{2}\end{vmatrix}\\\sf{det~P=8+1=9}\\\sf{P_x}=\begin{vmatrix}\sf{6}&\sf{-1}\\\sf{15}&\sf{2}\end{vmatrix}\\\sf{det~P_x=12+15=27}\\\sf{P_y}=\begin{vmatrix}\sf{4}&\sf{6}\\\sf{1}&\sf{15}\end{vmatrix}\\\sf{det~P_y=60-6=54}\\\sf{x=\dfrac{det~P_x}{det~P}=\dfrac{27}{9}=3}\\\sf{y=\dfrac{det~P_y}{P}=\dfrac{54}{9}=6}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{s=\{3,6\}}}}}}$