Question

verifique se r e s são paralelas:
r 3x - 4y - 2 = 0      s 6x - 8y + 1 = 0

r 5x - 3y + 1 = 0     s 6x + 4y - 1 = 0

Answer 1

Olá Marybia,

para que duas retas sejam paralelas entre si, devemos ter coeficientes angulares idênticos (coeficiente angular é o termo x da equação), portanto comparemos as duas retas simultaneamente:

$3x-4y-2=0~~~~~~~~~~~~~~~~~~~~6x-8y+1=0\\ 4y=3x-2~~~~~~~~~~~~~~~~~~~~~~~~~8y=6x+1\\\\ y= \dfrac{3x-2}{4}~~~~~~~~~~~~~~~~~~~~~~~~~~y= \dfrac{6x+1}{8}\\\\ y= \dfrac{3}{4}x- \dfrac{2}{4}~~~~~~~~~~~~~~~~~~~~~~~~~y= \dfrac{6}{8}x+ \dfrac{1}{8}\\\\ y= \boxed{\dfrac{3}{4}x}- \dfrac{1}{2}~~~~~~~~~~~~~~~~~~~~~~~y= \boxed{\dfrac{3}{4}x}+ \dfrac{1}{8}\\\\\\ Portanto,~r\backslash\backslash s~~(r~e\´~paralela~a~s)$

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$5x-3y+1=0~~~~~~~~~~~~~~~~~~~~~6x+4y-1=0\\ 3y=5x+1~~~~~~~~~~~~~~~~~~~~~~~~~~6x-1=-4y\\\\ y= \dfrac{5x+1}{3} ~~~~~~~~~~~~~~~~~~~~~~~~~~-y= \dfrac{6x-1}{4}\\\\ y= \dfrac{5}{3}x+ \dfrac{1}{3}~~~~~~~~~~~~~~~~~~~~~~~~~~- y=\dfrac{6}{4}x- \dfrac{1}{4}\\\\ y= \boxed{\dfrac{5}{3}x}+ \dfrac{1}{3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y=\boxed{- \dfrac{3}{2}x}+ \dfrac{1}{4}\\\\\\ Portanto,~r~n\~ao~e\´~paralela~a~s$

Tenha ótimos estudos! ^^