Question

Resolva os sistemas de equações de 1 grau: pf com calculos
a) x+2y=5
2x+y=4
b) x+y=3
2x+3y=5
c) x+5y=7
3x-5y= 1
d) 4x-3y=5
3x+y =7
e) x+y=10
2x-y=8

Answer 1

a)

(I) x + 2y = 5

(II) 2x + y = 4

(I) x + 2y = 5

(I) x = 5 - 2y

(II) 2(5 - 2y) + y = 4

(II) 10 - 4y + y = 4

(II) 10 - 3y  = 4

(II) - 3y  = 4 - 10

(II) - 3y  = -6

(II) y  = 6/3

(II) y  = 2

(I) x + 2(2) = 5

(I) x + 4 = 5

(I) x = 5 - 4

(I) x = 1

b)

(I) x + y = 3

(II) 2x + 3y = 5

(I) y = 3 - x

(II) 2x + 3(3 - x) = 5

(II) 2x + 9 - 3x = 5

(II) -x = -4

(II) x = 4

(I) y = 3 - 4

(I) y = -1

c)

(I) x + 5y = 7

(II) 3x - 5y = 1

(I) x = 7  - 5y

(II) 3(7 - 5y) - 5y = 1

(II) 21 - 15y - 5y = 1

(II) - 20y = -20

(II) y = 1

(I) x = 7  - 5(1)

(I) x = 2

d)

(I) 4x - 3y = 5

(II) 3x + y = 7

(II) y = 7 - 3x

(I) 4x - 3(7 - 3x) = 5

(I) 4x - 21 + 9x = 5

(I) 13x = 26

(I) x = 2

(II) 3(2) + y = 7

(II) 6 + y = 7

(II) y = 1

e)

(I) x + y = 10

(II) 2x - y = 8

(I) x = 10 - y

(II) 2(10 - y) - y = 8

(II) 20 - 2y - y = 8

(II) - 3y = -12

(II) y = 12/3

(II) y = 4

(I) x = 10 - 4

(I) x = 6