Question

Resolva os sistemas de equações pelo método da substituição

Answer 1

Resposta:

a) 4x-y=2

-y=-4x+2

y=4x-2

3x+2(4x-2)=7

3x+8x-4=7

11x=7+4

x=1

Agora sabendo o valor de x:

y=4.1-2

y=4-2

y=2

===============

b) x+y=1

x-2y=1

x=1-y

(1-y)-2y=1

1-3y=1

-3y=0

y=0

x=1-0

x=1

===============

c) 5x-2y=1

2x-y=4

-y=4-2x

y=2x-4

5x-2(2x-4)=1

5x-4x+8=1

x=-7

y=4-2(-7)

y=4+14

y=18

===============

d) 2x-4y=-2

5x-3y=2

2x=4y-2

x=(4y-2)/2

x=2y-1

5(2y-1)-3y=2

10y-5-3y=2

7y=2+5

y=7/7

y=1

x=(2.1)-1

x=2-1

x=1

===============

e) 3x+5y=7

2x-3y=11

2x=11+3y

x=(11+3y)/2

3((11+3y)/2)+3y=11

(33+9y)/2+3y=11

33+9y+6y=11.2

15y=22-33

y=-11/15

x=(11+3(-11/15))/2

x=(11-33/15)/2

x=(165-33/15)/2

x=8.8/2

x=4.4

===============

f) x=y-2

2x+y=-1

2(y-2)+y=-1

2y-4+y=-1

3y=4-1

3y=3

y=1

x=1-2

x=-1

===============

g) 3x-2y=3

4y=12

4y=12

y=12/4

y=3

3x-2.3=3

3x-6=3

3x=6+3

3x=9

x=9/3

x=3

===============

h) 4x=2y

2x+3y=8

4x=2y

x=2y/4

x=½y

2.(½y)+3y=8

y+3y=8

4y=8

y=8/4

y=2

x=½.2

x=1

===============

i) 7x-3y=6

2x=y+3

2x-3=y

7x-3(2x-3)=6

7x-6x+9=6

x=-9+6

x=-3

2.(-3)-3=y

-6-3=y

y=-9

===============

j) x-y-2=0

2x+y=7

x=2+y

2(2+y)=7

4+2y=7

2y=7-4

y=3/2

x=2+3/2

x=4+3/2

x=7/2 ou 3,5