Question

Resolva os sistemas de equações pelo método da adição.
a) x – y = 3
3x + y = 17


b) 5x + 2y = 23
4x – 2y = 22

c) 2x + 3y = 8
3x + y = 17

d) – 2x + 2y = 2

+ 2x – 3y = – 5


e) 6x + 4y = 80
x – 4y = 10


f) 2x + 2y = 12
3x – 2y = 13

Answer 1

a)

{x – y = 3

{3x + y = 17

x+3x-y+y = 3+17

4x = 20

x = 20/4

x = 5

x-y = 3

5-y = 3

-y = 3-5

y = 2

S = {5,2}

b)

{5x + 2y = 23

{4x – 2y = 22

5x+4x = 22+23

9x = 45

x = 45/9

x = 5

5x+2y = 23

5(5)+2y = 23

25+2y = 23

2y = 23-25

2y = -2

y = -2/2

y = -1

S = {5,-1}

c)

{2x + 3y = 8

{3x + y = 17 ---- y = 17-3x

2x+3(17-3x) = 8

2x+51-9x = 8

2x-8x = 8-51

-7x = -43

x = 43/7

y = 17-3x

y = 17-3(43/7)

y = 17-129/7

y = -10/7

S = { 43/7,-10/7}

d)

{– 2x + 2y = 2

{+ 2x – 3y = – 5

-2x+2x+2y-3y = 2-5

-y = -3

y = 3

2x-3y = -5

2x-3(3) = -5

2x-9 = -5

2x = -5+9

2x = 4

x = 4/2

x = 2

S = {2,3}

e)

{6x + 4y = 80

{x – 4y = 10

6x+x+4y-4y = 10+80

7x = 90

x = 90/7

x-4y = 10

90/7-4y = 10

-4y = 10-90/7

-4y = -20/7

y = 5/7

S = {90/7,5/7)

f)

{2x + 2y = 12

{3x – 2y = 13

2x+3x+2y-2y = 12+13

5x = 25

x = 25/5

x = 5

2x+2y = 12

2(5)+2y = 12

10+2y = 12

2y = 12-10

2y = 2

y = 2/2

y = 1

S = {5,1}

Prontinho ❤️❤️

02/11/21