Question

Alguém pra me ajudar????

Letra :

E       F

Answer 1

e)
$\left \{ {{2x- \frac{y-3}{2}=4 } \atop {3y- \frac{x-2}{3}=9 }} \right.$

$\left \{ {4x-(y-3)=8} \atop {9y-(x-2)=27}} \right.$

$\left \{ {{4x-y+3=8} \atop {9y-x+2=27}} \right.$

$\left \{ {{4x-y=8-3} \atop {-x+9y=27-2}} \right.$

$\left \{ {{4x-y=5} \atop {-x+9y=25}} \right.$

adição (×4) a 2°

$\left \{ {{4x-y=5} \atop {-4x+36y=100}} \right.$

cancela o y e soma

$35y=105 \\ y=105\div35 \\ y=3$

substituir y em

$4x-y=5 \\ 4x-3=5 \\ 4x=5+3 \\ 4x=8 \\ x=8\div4 \\ x=2$

S={(2,3)}


f)
$\left \{ {{5-15x=4+2y-2} \atop {12x-5=3-24y}} \right.$

$\left \{ {{-15x-2y=4-2-5} \atop {12x+24y=3+5}} \right.$

$\left \{ {{-15x-2y=-3} \atop {12x+24y=8}} \right.$

adição , (×12) a 1°

$\left \{ {{-180x-24y=-36} \atop {12x+24y=8}} \right.$

cancela o y e soma
fica

$-168x=-28 \\ 168x=28$

$x= \frac{28}{168} =\fbox{ \frac{1}{6} }$

substituir x em

$12x+24y=8 \\ 12( \frac{1}{6})+24y=8 \\ 2+24y=8 \\ 24y=8-2 \\ 24y=6$

$y= \frac{6}{24} =\fbox{ \frac{1}{4} }$

S={( $\frac{1}{6} , \frac{1}{4}$)}

Answer 2

e) $2x-\dfrac{y-3}{2}=4$

Simplificando:

$4x-y+3=8~~\Rightarrow~~4x-y=5~~\Rightarrow~~y=4x-5$

Substituindo na segunda equação:

$3y-\dfrac{x-2}{3}=9$

$3\cdot(4x-5)-\dfrac{x-2}{3}=9~~\Rightarrow~~9\cdot(4x-5)-x+2=27~~\Rightarrow~36x-45-x+2=27$

$35x=70~~\Rightarrow~~x=\dfrac{70}{35}~~\Rightarrow~~\boxed{x=2}$

$y=4x-5~~\Rightarrow~~y=4\cdot2-5~~\Rightarrow~~y=8-5~~\Rightarrow~~\boxed{y=3}$

$S=\{2,3\}$


f) $5(1-3x)=4+2(y-1)$

Simplificando:

$5-15x=4+2y-2~~\Rightarrow~~2y=5+2-4-15x~~\Rightarrow~~2y=3-15x$.

Daí, $8y=4(3-15x)~~\Rightarrow~~8y=12-60x$

Substituindo na segunda equação:

$12x-5=3(1-8y)$

$12x-5=3\cdot(1-12+60x)~~\Rightarrow~~12x-5=180x-33~~\Rightarrow~~168x=28$

$x=\dfrac{28}{168}~~\Rightarrow~~\boxed{x=\dfrac{1}{6}}$

$2y=3-15x~~\Rightarrow~~y=\dfrac{3-15x}{2}~~\Rightarrow~~y=\dfrac{3-15\cdot\frac{1}{6}}{2}$

$y=\dfrac{3-\frac{15}{6}}{2}~~\Rightarrow~~y=\dfrac{\frac{18-15}{6}}{2}$

$y=\dfrac{\frac{3}{6}}{2}~~\Rightarrow~~y=\dfrac{3}{12}~~\Rightarrow~~\boxed{y=\dfrac{1}{4}}$

$S=\{\frac{1}{6},\frac{1}{4}\}$.