Question

resolva os sistemas de equação abaixo utilizando a técnica da substituição


A) x+3y=6
2x+y=-3

B) 4x-2y=8
-x+y=6

C) x-y=12
4x+y=3

D) 2x-4y=5
3x+2y=8​

Answer 1

A) {x+3y=6

{2x+y=-3

x + 3y = 6

x = 6 - 3y

2x + y = -3

2 . (6 - 3y) + y = -3

12 - 6y + y = -3

12 - 5y = -3

-5y = -3 - 12

-5y = -15

y = -15/-5

y = 3

x + 3y = 6

x + 3 . 3 = 6

x + 9 = 6

x = 6 - 9

x = -3

B) {4x-2y=8

{-x+y=6

-x + y = 6

y = 6 + x

4x - 2y = 8

4x - 2 . (6 + x) = 8

4x - 12 - 2x = 8

2x - 12 = 8

2x = 8 + 12

2x = 20

x = 20/2

x = 10

-x + y = 6

-10 + y = 6

y = 6 + 10

y = 16

C) {x-y=12

{4x+y=3

x - y = 12

x = 12 + y

4x + y = 3

4 . (12 + y) + y = 3

48 + 4y + y = 3

48 + 5y = 3

5y = 3 - 48

5y = -45

y = -45/5

y = -9

x - y = 12

x - (-9) = 12

x + 9 = 12

x = 12 - 9

x = 3

D) {2x-4y=5

{3x+2y=8

2x - 4y = 5

2x = 5 + 4y

x = 5 + 4y /2

3x + 2y = 8

3 . (5 + 4y) /2 + 2y = 8

15 + 12y /2 + 2y = 8

15 + 12y + 2.2y /2 = 8

15 + 12y + 4y /2 = 8

15 + 16y /2 = 8

15 + 16y = 8 . 2

15 + 16y = 16

16y = 16 - 15

16y = 1

y = 1/16

2x - 4y = 5

2x - 4 . 1/16 = 5

2x - 4/16 = 5

2x = 5 + 4/16

2x = 16.5/16 + 4/16

2x = 80/16 + 4/16

2x = 84/16

x = 84/16 ÷ 2

x = 84/16 . 1/2

x = 84/32

x = 21/8