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gladu [14]
3 years ago
10

Solve the following system for all solutions: (x - 1)^2 + (y + 3)^2 = 13 x + y = -3​

Mathematics
1 answer:
Mamont248 [21]3 years ago
4 0

Answer:

  • ( -4, -1 ) and ( -9, - 6)

Step-by-step explanation:

<h3>Given</h3>
  • (x - 1)^2 + (y + 3)^2 = 13
  • x + y = -3​
<h3>Solution</h3>

<u>From the second equation we get</u>

  • x = - y - 3

<u>Substituting x in the first equation</u>

  • (- y - 3 - 1)^2 + (y + 3)^2 = 13
  • (-y - 4)^2 + (y + 3)^2 = 13
  • (y+4)^2 + (y+3)^2 = 13
  • y^2 + 8y + 16 + y^2 + 6y + 9 = 13
  • 2y^2 + 14y + 12 = 0
  • y^2 +7y +6 = 0
  • (y+1)(y+6) = 0
  • y = - 1
  • y = - 6

<u>Then</u>

  • x = -4
  • x = - 9

<u>Answer</u>

  • ( -4, -1 ) and ( -9, - 6)
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