Question

as retas (r) 2x+y=3 e (s)2x+ay=5 são paralelas então:

a)a=-3

b)a=-2

c)a=-1

d)a=1

e)a=2​

Answer 1

Se duas retas são paralelas então seus coeficientes angulares são iguais. Então basta isolar o y e igualar os coeficientes angulares :

$\displaystyle \text I) \ 2\text x+\text y=3 \\\\\ \ \ \text y=-2\text x+3\\\\\ \boxed{\text{coef. angular }=-2} \\\\\\ 2\text x+\text {a.y} =5\\\\\ \text a.\text y = -2\text x+5\\\\ \text y = \frac{-2\text x}{\text a}+\frac{5}{\text a}\\\\ \boxed{\text{coef. angular } = \frac{-2}{\text a}}$

Igualando os coeficientes angulares :

$\displaystyle -2=\frac{-2}{\text a} \\\\ \huge\boxed{\text a =1}\\\\ \text{letra (d)}$