Question

resolva a equação pelo método da substituição {4x+5y = 26 { y = x-3

Answer 1

$\begin{array}{l}\mathsf{S=}\left\{\begin{matrix}\mathsf{4x+5y=26~~~~(i)}\\\\\mathsf{y=x-3~~~(ii)}~~~~ \end{matrix}\right.\\\\\\\mathsf{Substituindo~y~em~(i)~teremos~o~seguinte:}\\\\\\\mathsf{(i)~~4x+5(x-3)=26}\\\\\mathsf{(i)~~4x+5x-15=26}\\\\\mathsf{(i)~~9x-15=26}\\\\\mathsf{(i)~~9x=26+15}\\\\\mathsf{(i)~~9x=41}\\\\\mathsf{(i)~~x= \dfrac{41}{9}}\end{array}$


$\begin{array}{l}\mathsf{Substituindo~x~em~(ii),~teremos~o~seguinte:}\\\\\\\mathsf{(ii)~~y=\dfrac{41}{9}-3~~~~(reduzindo~a~um~denominador~comum...)}\\\\\\\mathsf{(ii)~~y=\dfrac{41}{9}- \dfrac{27}{9}}\\\\\\\mathsf{(ii)~~y=\dfrac{14}{9}}\\\\\\\\\mathsf{Solu\c{c}\~ao=\left\{\begin{matrix}\mathsf{x=\dfrac{41}{9} }\\\\\\\mathsf{y=\dfrac{14}{9} } \end{matrix}\right.}\end{array}$