Question

Resolva os sistemas de equações

Answer 1

Olá!!

Resolução!!

J)

{x + y = 6

{x - y = 2

=======

2x = 8

x = 8/2

x = 4

x + y = 6

4 + y = 6

y = 6 - 4

y = 2

S={ 4, 2}

==============================

D)

{ 2x + 2y = 22

{ x = y + 5

=========

2.(y + 5) + 2y = 22

2y + 10 + 2y = 22

4y = 12

y = 12/4

y = 3

x = y + 5

x = 3 + 5

x = 8

S={ 8, 3 }

________________________________________

E)

{ x + y = 60

{ x = 2y

========

2y + y = 60

3y = 60

y = 60/3

y = 20

x = 2y

x = 2.20

x = 40

S={ 40, 20 }

_______________________________________

_

F)

{ x + y = 9

{ x - y = 3

========

2x = 12

x = 12/2

x = 6

x + y = 9

6 + y = 9

y = 9 - 6

y = 3

S={ 6, 3 }

_________________________________________

G)

{ x + y = 100

{ x = 2y + 4

=========

2y + 4 + y = 100

2y + y = 100 - 4

3y = 96

y = 96/3

y = 32

x = 2y + 4

x = 2.32 + 4

x = 64 + 4

x = 68

S={ 68, 32 }

_________________________________________

Eaí foi rápido?! rsrs

★Espero ter ajudado!! Tmj.

Answer 2

Resposta

$a) S= \left\{32,80\right\}$    $b) \left\{5,18\right\}$         $c) S = \left\{-3,17\right\}$      $d) S= \left\{8,3\right\}$    $e) S= \LEFT\{40,20\RIGHT\}$    $f) S={\left\{6,3\right\}$    $g) S = \left\{68,32\right\}$       $h) S = \left\{8,16\right\}$          $i) \left\{\frac{46}{7},\frac{71}{7}\right\}$  $j) S = \left\{4,2\right\}$    

Sistemas de Equação de 1º Grau

Método da Substituição (todos menos f e j)

$a) \left \{ {{v+ g=112} \atop {4v+ 2g=384}} \right.$

   $v = 112 - g$

   $4 (112-g) + 2g = 384\therefore 448 - 4g + 2g = 384 \therefore -2g = 384 - 448$

  $-2g = -64 \therefore g = -64 : -2 \therefore g = 32$

   Calculando v:

    $v = 112 - g \therefore v = 112 - 32 \therefore v = 80$

    $S= \left\{32,80\right\}$

$b) \left \{ {{x+y=23} \atop {2x+4y=82}} \right.$

     $x = 23 - y$

     $2(23 -y) + 4y = 82\therefore 46 - 2y + 4y = 82 \therefore 2y = 82 - 46$

    $2y = 36 \therefore y = 36 : 2 \therefore y = 18$

   Calculando x:

   $x = 23 - y \therefore x = 23 - 18 \therefore x = 5$

   $S = \left\{5,18\right\}$

$c) \left \{ {{x+y=14} \atop {4x+2y=22}} \right.$

    $x = 14 - y$

    $4(14-y)+2y = 22\therefore 56 - 4y + 2y = 22\therefore -2y = 22-56\therefore -2y=-34$

    $y = -34 : -2\therefore y = 17$

   Calculando x:

    $x = 14 - y \therefore x = 14 - 17 \therefore x= -3$

    $S = \left\{-3,17\right\}$

$d) \left \{ {{2x+2y=22} \atop {x= y+5}} \right.$

 $2(y+5) + 2y = 22 \therefore 2y+10 +2y = 22\therefore 4y = 22 -10$

 $4y = 12\therefore y = 12 : 4 \therefore y = 3$

  $x = y + 5 \therefore x = 3 + 5 \therefore x = 8$

  $S = \left\{8,3\right\}$

$e) \left \{ {{x+y=60} \atop {x=2y}} \right.$

    $2y + y = 60\therefore 3y = 60 \therefore y = 60:3\therefore y = 20$

    $x = 2y \therefore x = 2.20 \therefore x = 40$

    $S = \left\{40,20\right\}$

$f) \left \{ {{x+y=9} \atop {x-y=3}} \right.$

   $x + x + y - y = 9 + 3\therefore 2x = 12 \therefore x = 12 : 2 \therefore x = 6$

   $x + y= 9 \therefore y = 9 - x \therefore y = 9 - 6 \therefore y = 3$

   $S = \left\{6,3\right\}$

$g) \left \{ {{x+y=100} \atop {x=2y+4}} \right.$

    $(2y+4)+y = 100\therefore 2y+4+y = 100 \therefore 3y = 100 - 4\therefore 3y = 96$

    $y = 96 : 3\therefore y = 32$

    Calculando x:

    $x + y = 100\therefore x + 32 = 100 \therefore x = 100 - 32\therefore x= 68$

    $S= \left\{68,32\right\}$

$h) \left \{ {{x+y=24} \atop {3x+3y=56}} \right.$

    $x = 24 -y$

    Calculando y:

    $3(24-y) + 2y = 56\therefore 72 - 3y + 2y = 56$

    $- y= 56 - 72 \therefore -y = -16 \therefore y = 16$

    Calculando x:

    $x = 24 - y \therefore x = 24 - 16 \therefore x = 8$

    $S = \left\{8,16\right\}$

$i) \left \{ {{2x-y=3} \atop {3x-5y=-31}} \right.$

   Isolando y na primeira equação:

    $2x - y = 3 \therefore -y = 3 - 2x \therefore y = 2x - 3$

    substituindo x na segunda equação:

    $3x - 5 (2x-3) = - 31\therefore 3x - 10x + 15 = - 31$

    $-7x =-31 - 15 \therefore -7x = -46 \therefore x = \frac{46}7}$

    Calculando y:

    $y = 2.\frac{46}{7}-3\therefore y = \frac{92}{7}-3 \therefore y = \frac{92-21}{7} \therefore y = \frac{71}{7}$    

    $S = \left\{\frac{46}{7},\frac{71}{7}\right\}$

$j) \left \{ {{x+y=6} \atop {x-y=2}} \right.$

 

   $x + x + y - y = 6 + 2$

   $2x = 8$

   $x = 8 : 2$

   $x = 4$

   Calculando y:

   $x + y = 6\\y = 6 - x\\y = 6-4\\y = 2$

   $S=\left\{4,2\right\}$

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