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The three lines given below form a triangle. Find the coordinates of the vertices of the triangle.

Line 1: -3x + 2y = 1 Line 2: 2x + y = 11 Line 3: x + 4y = 9

Respuesta :

mhanifa

Answer:

  • (3, 5), (1, 2) and (5, 1)

Step-by-step explanation:

Make three systems with pairs of lines and solve them to work out the vertices.

1) Line 1 and line 2

  • -3x + 2y = 1
  • 2x + y = 11

Double the second equation and subtract equations:

  • -3x + 2y - 2(2x + y) = 1 - 2(11)
  • -3x - 4x = 1 - 22
  • -7x = - 21
  • x = 3

Find y:

  • 2*3 + y = 11
  • 6 + y = 11
  • y = 11 - 6
  • y = 5

The point is (3, 5)

2) Line 1 and line 3

  • -3x + 2y = 1
  • x + 4y = 9

Triple the second equation and add up equations:

  • -3x + 2y + 3(x + 4y) = 1 + 3(9)
  • 2y + 12y = 1 + 27
  • 14y = 28
  • y = 2

Find x:

  • x + 4*2 = 9
  • x + 8 = 9
  • x = 1

The point is (1, 2)

3) Line 2 and line 3

  • 2x + y = 11
  • x + 4y = 9

Double the second equation and subtract the equations:

  • 2x + y - 2(x + 4y) = 11 - 2(9)
  • y - 8y = 11 - 18
  • - 7y = - 7
  • y = 1

Find x:

  • x + 4*1 = 9
  • x + 4 = 9
  • x = 5

The point is (5, 1)

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