Question

Obtenha o ponto de intersecção entre as retas:
A)x-5y-14=0 e 3x+2y+9=0
B) x+2y-6=0 e 2x -y+4=0
C) x+2y+5=0 e 3x-3y+1=0

Answer 1

a)

x - 5y - 14 = 0
3x + 2y + 9 = 0

x - 5y = 14
3x + 2y = -9

-3x + 15y = - 42
3x + 2y = - 9

17y = -51
y= -51/17
y = -3

x - 5y = 14
x - 5.(-3) = 14
x + 15 = 14
x = 14- 15
x = - 1

P(-1,-3)
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b)

x + 2y - 6 = 0
2x - y + 4 = 0

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

-2x - 4y = -12
2x - y = - 4

-5y = -16

y = 16/5

x + 2y = 6
x + 2 . 16/5 = 6

x + 32/5 = 6

5x + 32 = 30
5x = 30 - 32
x = - 2/5

P(-2/5, 16/5)
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x)

x + 2y + 5 = 0
3x - 3y + 1 = 0

x + 2y = - 5
3x - 3y = - 1

-3x - 6y = 15
3x - 3y = - 1

- 9y = 14
y = -14/9

x + 2y = - 5

x + 2 . (-14/9) = - 5

x - 28/9 = - 5

9x - 28 = - 45

9x = - 45 + 28

9x = -17

x = - 17/9

P(-17/9, -14/9)