Question

Resolva os sistemas de equação:
a)x+y=-2
2x-y=26

b)2x+y=5
3x-y=10

c)x+y=6
x-y=2

d)2x-2y=12
x+2y=11

e)2x+2y=4
3x-2y=1

f)5x-y=7
2x+y=7

g)x+y=20
x-y=8

Answer 1

Método da Adição (em todas):

a)
x + y = - 2
2x - y = 26 (+)
--------------------
3x = 24
x = 24/3
x = 8

x + y = - 2
8 + y = - 2
y = - 2 - 8
y = - 10

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)

2x + y = 5
3x - y = 10  (+)
--------------------
5x = 15
x = 15/5
x = 3

2x + y = 5
2.3 + y = 5
6 + y = 5
y = 5 - 6
y = - 1

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
x + y = 6
x - y = 2  (+)
------------------
2x = 8
x = 8/2
x = 4

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


*******************************
d)
2x - 2y = 12
x + 2y = 11    (+)
---------------------
3x = 23
x = 23
     ------
        3

x + 2y = 11
23  + 2y = 11
-----
  3

23 + 6y = 33
----------   -----
    3           3

23 + 6y = 33
6y = 33 - 23
6y = 10

y =  10   (:2)
      ------
        6    (:2)

y =  5
     -----
       3
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨

e)
2x + 2y = 4
3x - 2y = 1  (+)
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
5x = 5
x = 5/5
x = 1

2x + 2y = 4
2.1 + 2y = 4
2 + 2y = 4
2y = 4 - 2
2y = 2
y = 2/2
y = 1

****************************
f)
5x - y = 7
2x + y = 7¨ (+)
-------------------
7x = 14
x = 14/7
x = 2

2x + y = 7
2.2 + y = 7
4 + y = 7
y = 7 - 4
y = 3

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
g)
x + y = 20
x - y = 8    (+)
------------------------
2x = 28
x = 28/2
x = 14

x + y = 20
14 + y = 20
y = 20 - 14
y = 6


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