Question

(URGENTE) Resolva os sistemas de equações usando o método da substituição.
a. x+3y=6
2x+y=-3

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

c. x-2y = -7
2x+2y= 1

D. 2x - y = 4
3x + 2y = 6

E. 3x-y =0
-4x+y = -2

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

-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

-x = 6 - y

x = -6 + y

4x - 2y = 8

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

-24 + 4y - 2y = 8

4y - 2y = 8 + 24

2y = 32

y = 32/2

y = 16

-x + y = 6

-x + 16 = 6

-x = 6 - 16

-x = -10

x = 10

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

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

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

15 + 12y/2 + 2y = 8

mmc

2 , 1 2

1 , 1 / 2

15 + 12y/2 + 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

mmc

1 , 16 2

1 , 8 2

1 , 4 2

1 , 2 2

1 , 1 / 2 . 2 . 2 . 2 = 16

2x = 16.5/16 + 4/16

2x = 80/16 + 4/16

2x = 84/16

2x = 21/4

x = 21/4 ÷ 2

x = 21/4 . 1/2

x = 21/8

d. {2x - y = 4}

{3x + 2y = 6}

2x - y = 4

2x - 4 = y

3x + 2 . (2x - 4) = 6

3x + 4x - 8 = 6

7x = 6 + 8

7x = 14

x = 14/7

x = 2

2x - y = 4

2 . 2 - y = 4

4 - y = 4

4 - 4 = y

0 = y

e) {3x-y =0}

{-4x+y = -2}

3x - y = 0

3x - 0 = y

-4x + y = -2

-4x + 3x - 0 = -2

3x + 2 = 4x

2 = 4x - 3x

2 = x

3x - y = 0

3 . 2 - y = 0

6 - y = 0

6 = y