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algebraically find the x-coordinates where the line y=2x+3 intersects the circle (x-3)^2 + (y+6)= 50
** please help its due soon **

Respuesta :

mhanifa

Answer:

  • x = {-4, -2}

Step-by-step explanation:

To find the intersection we need to solve the system:

  • y = 2x + 3
  • (x - 3)² + (y + 6)² = 50

Solve by substitution, replace y with 2x + 3 in the second equation:

  • (x - 3)² + (2x + 3 + 6)² = 50
  • x² - 6x + 9 + 4x² + 36x + 81 - 50 = 0
  • 5x² + 30x + 40 = 0
  • x² + 6x + 8 = 0
  • x² + 6x + 9 = 1
  • (x + 3)² = 1
  • x + 3 = ± 1
  • x = -4, x = -2

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