Question

nos sistemas abaixo o valor de x e y é:
a)
x - 2y = 3
2x - 3y = 5
b)
4x + 2y = 16
5x - 3 y = 9
c)
5 (x+1) + 3 (y-2) = 4
8 (x+1) + 5 (y-2) = 9

Answer 1

a)

x - 2y = 3 → x = 3 + 2y

2x - 3y = 5 → 2(3 + 2y) - 3y = 5 → 6 + 4y - 3y = 5 → y = 5 - 6 → y = -1

x - 2y = 3 → x - 2(-1) = 3 → x + 2= 3 → x = 3 -2 → x = 1

b)

4x + 2y = 16 → 4x = 16 - 2y → x = (16 - 2y)/4 → x = 4 - 1/2y

5x - 3 y = 9 → 5(4 - 1/2y) - 3y = 9 → 20 - 5/2y - 3y = 9 → -5/2y - 6/2y = 9 - 20 → -11/2y = -11 → 11y = 11•2 → 11y = 22 → y = 22/11 → y = 2

4x + 2y = 16 → 4x + 2(2) = 16 → 4x + 4 = 16 → 4x = 16-4 → 4x = 12 → x = 12/4 → x = 3

c)

5 (x+1) + 3 (y-2) = 4

5x+5 + 3y-6 = 4

5x+3y-1 = 4

5x+3y = 5

5x = 5 - 3y

x = (5-3y)/5

x = 1-0,6y

8 (x+1) + 5 (y-2) = 9

8x+8+5y-10 = 9

8x+5y-2 = 9

8x+5y = 11

8(1-0,6y)+5y = 11

8-4,8y+5y = 11

0,2y = 11-8

0,2y = 3

y = 3/0,2

y = 15

x = 1-0,6y

x = 1-0,6(15)

x = 1-9

x = -8