Question

Aplicando o método da comparação, resolva os seguintes sistemas:

a) x - y = 1
-x + 2y= 3

b) x =3y
x - 2y = 3

c) 2x + y = -3
x + y = -1

Answer 1

$A)~~~~\begin{cases}x-y=1\\ -x+2y=3\end{cases}\\\\\\\\ x-y=1\to~~ x=y+1\\\\\\\\ -x+2y=3\to~~ -x=-2y+3~~(-1)\to~~x=2y-3\\\\\\\\ y+1=2y-3\to~~ y-2y=-3-1\to~~ -y=-4~~(-1)\to ~~\large\boxed{y=4}\\\\\\\\ x=y+1\to~~x=4+1\to~~\large\boxed{x=5} \\\\\\\\\\ \Large\boxed{\boxed{S=\{5~;~4\}}}$








$B)~~~~\begin{cases}x=3y\\ x-2y=3\end{cases}\\\\\\\\ x-2y=3\to~~x=2y+3\\\\\\\\ 3y=2y+3\to~~ 3y-2y=3\to~~ \large\boxed{y=3}\\\\\\\\ x=3y\to~~ x=3*3\to~~\large\boxed{x=9} \\\\\\\\\\ \large\boxed{\boxed{S=\{9~;~3\}}}$








$\begin{cases}2x+y=-3\\ x+y=-1\end{cases}\\\\\\\\ 2x+y=-3\to~~ 2x=-y-3\to~~ x= \dfrac{-y-3}{2}\\\\\\\\ x+y=-1\to~~x=-y-1\\\\\\\\ \dfrac{-y-3}{2}=-y-1\to~~ multiplique~~cruzado:\\\\ -y-3=-2y-2\to~~ -y+2y=-2+3\to~~ \large\boxed{y=1}\\\\\\\\ x=-y-1\to~~ x=-1-1\to~~ \large\boxed{x=-2} \\\\ \\\\\\ \large\boxed{\boxed{S=\{-2~;~1\}}}$