Question

resolva os sistemas pelo método da substituição .

a) x+y=22
x-y=8

b) x+y=4
3x+y=28

c) -2x-3y=-9
x+4y=12

d) -6x+2y=8
9x-y=8​

Answer 1

Resposta:

a) x + y = 22

x - y = 8

x = 8 + y

(8 + y) + y = 22

8 + 2 y = 22

2 y = 22 - 8

y = 14/2

y = 7

x - y = 8

x - 7 = 8

x = 8 + 7

x = 15

b) x + y = 4

3 x + y = 28

x = 4 - y

3 (4 - y) + y =28

12 - 3 y +y = 28

12 - 2 y = 28

12 - 28 = 2y

2 y = 12 - 28

y = - 16

x+y=4

x -16 = 4

x = 4 + 16

x = 20

c) - 2 x - 3 y = - 9

x + 4 y = 12

x = 12 - 4y

-2 (12 - 4y ) - 3 y = - 9

-24 + 8 y - 3 y = - 9

5 y = - 9 + 24

y = 15/5

y = 3

x + 4 y = 12

x + 4 . - 3 = 12

x + 12 = 12

x = 12 - 12

x = 0

 

d) - 6 x + 2 y = 8

9 x - y = 8​

- y = 8 - 9 x

y = - 8 + 9 x

- 6 x + 2 (- 8 + 9 x) = 8  

- 6 x - 16 + 18 x = 8

18 x - 6 x = 8 + 16

12 x = 24

x = 24/12

x = 2

9 x - y =8​

9 . 2 - y = 8

18 - y = 8

18 - 8 = y

y = 10