Question

Sistemas de equações:

A) 2x + y = 13
3x - y = 17


B) 4x + y = 11
2x - y = 1


C) 4x + y = 22
x - y = 3


D) x + y = 25
2x - y = 5


E) x + y = 10
3x - y = 14


F) 5x + y = 5
2x - y = 2

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Answer 1

A) 2x + y = 13

   3x - y = 17

2x + y = 13

y = 13 - 2x

3x - y = 17

3x - (13 - 2x) = 17

3x - 13 + 2x = 17

3x + 2x = 17 + 13

5x = 30

x = 30 / 5

x = 6

y = 13 - 2x

y = 13 - 2 . 6

y = 13 - 12

y = 1

B) 4x + y = 11

   2x - y = 1

4x + y = 11

y = 11 - 4x

2x - y = 1

2x - (11 - 4x) = 1

2x - 11 + 4x = 1

2x - 11 + 4x = 1

2x + 4x = 1 + 11

6x = 12

x = 12 / 6

x = 2

y = 11 - 4x

y = 11 - 4 . 2

y = 11 - 8

y = 3

C) 4x + y = 22

    x - y = 3

4x + y = 22

y = 22 - 4x

x - y = 3

x - (22 - 4x) = 3

x - 22 + 4x = 3

x + 4x = 3 + 22

5x = 25

x = 25 / 5

x = 5

y = 22 - 4x

y = 22 - 4 . 5

y = 22 - 20

y = 2

D) x + y = 25

   2x - y = 5

x + y = 25

y = 25 - x

2x - y = 5

2x - (25 - x) = 5

2x - 25 + x = 5

2x + x = 5 + 25

3x = 30

x = 30 / 3

x = 10

y = 25 - x

y = 25 - 10

y = 15

E) x + y = 10

   3x - y = 14

x + y = 10

y = 10 - x

3x - y = 14

3x - (10 - x) = 14

3x - 10 + x = 14

3x + x = 14 + 10

4x = 24

x = 24 / 4

x = 6

y = 10 - x

y = 10 - 6

y = 4

F) 5x + y = 5

   2x - y = 2

5x + y = 5

y = 5 - 5x

2x - y = 2

2x - (5 - 5x) = 2

2x - 5 + 5x = 2

2x + 5x = 2 + 5

7x = 7

x = 7 / 7

x = 1

y = 5 - 5x

y = 5 - 5 . 1

y = 5 - 5

y = 0