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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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Because the axis of symmetry is -3, we know where to place our line, and we also know that the parabola is open downwards, which means that the vertex will be maximum. To find the vertex, plug in your values with the axis of symmetry as a midway point. Plug that in for x and so you should have the following:
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