Question

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Resolva os sistemas no metodo da adiçao*
a) 2x + y = 10
3x - 2y = 1

b) 2x + 3y = 10
4x - y = -1

c) x + y = 20
2x + 4y = 56

d) x + y = 23
2x + 4y = 82

e) x + y = 25
x - y = 13

f) x = 3y
x + y = 100

g) x = 2y
x + y = 30

h) x + y = 4
2x - 3y = 3

i) x + y = 17
6x = 7y + 24

j) 2x + 3y = 19
x - y = -3

Answer 1

a)
2x + y = 10  (2)
3x - 2y = 1

4x + 2y = 20
3x - 2y = 1    (+)
------------------------
7x = 21
x = 21/7
x = 3

2x + y = 10
2.3 + y = 10
6 + y = 10
y = 10 - 6
y = 4

***************************
b)
2x + 3y = 10
4x - y = - 1      (3)

2x + 3y = 10
12x - 3y = - 3  (+)
----------------------------
14x = 7
x =    7   (:7)
       ------
         14  (:7)

x =  1
      -----
        2

4x - y = - 1
4. 1  - y = - 1
   ----
     2

4/2 - y = - 1
2 - y = - 1
2 + 1 = y
3 = y
y = 3

*****************************
c)
x + y = 20       (-2)
2x + 4y = 56

- 2x - 2y = - 40
  2x + 4y = 56     (+)
-----------------------------
        2y =  16
         y = 16/2
         y = 8

x + y = 20
x + 8 = 20
x = 20 - 8
x = 12

********************************

d)
x + y = 23        (-2)
2x + 4y = 82

- 2x - 2y = - 46
  2x + 4y = 82
---------------------------
          2y = 36
           y = 36/2
           y = 18

x + y = 23
x + 18 = 13
x = 23 - 18
x = 5

******************************
e)
x + y = 25
x - y = 13  (+)
---------------------------
2x = 38
x = 38/2
x = 19

x + y = 25
19 + y = 25
y = 25 - 19
y = 6

********************************

f)
x = 3y
x + y = 100

x + y = 100
3y + y = 100
4y = 100
y = 100/4
y = 25

x = 3y
x = 3.25
x = 75

***************************
g)
x = 2y 
x + y = 30

x + y = 30
2y + y = 30
3y =30
y = 30/3
y = 10

x = 2y
x = 2.10
x = 20

*******************************
h)
x + y = 4      (3)
2x - 3y = 3

3x + 3y = 12
2x - 3y = 3    (+)
---------------------
5x = 15
x = 15/5
x = 3

x + y = 4
3 + y = 4
y = 4 - 3
y = 1

********************************************
i)
x + y = 17
6x = 7y + 24

x + y = 17      (7)
6x - 7y = 24

7x + 7y = 119
 6x - 7y = 24
-----------------------
 13x = 143
x = 143/13
x = 11

x + y = 17
11 + y = 17
y = 17 -11
y = 6

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
j)
2x + 3y = 19
x - y = - 3          (3)

2x + 3y = 19
3x - 3y = 9    (+)
-------------------------
 5x = 28
x =  28
       -----
         5 

x - y = - 3
28   -  y =  - 3
-----
  5

28 - 5y = - 3.5
----------   --------
     5            5

28 - 5y = - 15
28 + 15 = 5y
43 = 5y
5y = 43
y = 43
      ------
        5