Question

SÓ AS LETRAS       E       F       POR FAVOR

Answer 1

e) $\dfrac{x-2}{3}+\dfrac{y}{2}=\dfrac{1}{2}$

Simplificando:

$2(x-2)+3y=3$

$2x-4+3y=3~~\Rightarrow~~~2x=7-3y$


$x-1-\dfrac{y-1}{2}=1$

$2x-2-y+1=2$

Substituindo $2x$ por $7-3y$:

$7-3y-2-y+1=2$

$6-4y=2~~\Rightarrow~~4y=4~~\Rightarrow~~\boxed{y=1}$.

$2x=7-3y~~\Rightarrow~~2x=7-3~~\Rightarrow~~2x=4$

$x=\dfrac{4}{2}~~\Rightarrow~~\boxed{x=2}$

$S=\{2,1\}$


f) $\dfrac{2x+3y}{5}=10-\dfrac{y}{3}$

Simplificando:

$6x+9y=150-5y$

$6x=150-14y~~\Rightarrow~~3x=75-7y$

$\dfrac{4y-3x}{6}=\dfrac{3x}{4}+1$

Substituindo $3x$ por $75-7y$:

$\dfrac{4y-75+7y}{6}=\dfrac{75-7y}{4}+1$

$8y-150+14y=225-21y+12$

$43y=387~~\Rightarrow~~y=\dfrac{387}{43}~~\Rightarrow~~\boxed{y=9}$

$3x=75-7y~~\Rightarrow~~3x=75-7\cdot9~~\Rightarrow~~3x=75-63$

$3x=12~~\Rightarrow~~x=\dfrac{12}{3}~~\Rightarrow~~\boxed{x=4}$

$S=\{4,9\}$