Question

Resolva o sistema pelo metodo da substituiçao.
x -3 = -y 3x +2 = y+3

Answer 1

$\texttt{Reordene os termos da primeira equa\c{c}\~ao:} \\\\ x - 3 = -y~~ (some~y~em~ambos~os~membros~da~igualdade)\\\\ x + y - 3 = -y\hspace{-7}\diagup + y\hspace{-7}\diagup\\\\x+y-3=0~(some~3~em~ambos~os~membros~da~igualdade)\\\\x+y-3\hspace{-7}\diagup+3\hspace{-7}\diagup=0+3\\\\x + y = 3~(some~(-y)~em~ambos~os~lados~da~ igualdade)\\\\x + y + (-y) = 3+ (-y)\\\\x+y\hspace{-6}\diagup-y\hspace{-6}\diagup=3-y\\\\\fbox{ x=3-y }$


$\texttt{Substitua x na segunda equa\c{c}\~ao para descobrir y:}\\\\ \texttt{Equa\c{c}\~ao 2:}~~3x+2=y+3\\\\3\cdot(3-y)+2=y+3~(aplique~a~propriedade~distributiva)\\\\9-3y+2=y+3\\\\11-3y=y+3~(some~(-3)~em~ambos~os~membros~da~igualdade)\\\\(11+(-3))-3y=y+3+(-3)\\\\(11-3)-3y=y+3\hspace{-7}\diagup-3\hspace{-7}\diagup\\\\8-3y=y~(some~(-8)~em~ambos~os~membros~da~igualdade)\\\\(8+(-8))-3y=y+(-8)\\\\8\hspace{-7}\diagup-8\hspace{-7}\diagup-3y=y-8\\\\-3y=y-8~(some~(-y)~em~ambos~os~membros~da~igualdade)$

$-3y+(-y)=y+(-y)-8\\\\-3y-y=y\hspace{-6}\diagup-y\hspace{-6}\diagup-8\\\\-4y=-8~(divida~ambos~os~membros~da~igualdade~por~(-4))\\\\ \dfrac{-4\hspace{-5}\diagup y}{-4\hspace{-5}\diagup}=\dfrac{-8}{-4}\\\\\fbox{ y=2 }\\\\\texttt{Agora basta substituir y na primeira equa\c{c}\~ao e descobrir}\\\texttt{o valor de x:}\\\\ x+y=3\\\\x+2=3\\\\\fbox{ x=1 }$