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How many real solutions(intersections) will there be in the system of two equations

How many real solutions(intersections) will there be in the system of two equations-example-1

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Answer:

  • Two real solutions

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Given is the system of equations.

Solve it by elimination, multiply the first equation by 2 and second equation by - 5, then them add up:

  • 10x² + 4y² - 10x² - 25y² = 20 - 50
  • - 21y² = - 30
  • y² = 30/21
  • y² = 10/7
  • y = ±
    √(10/7)

Since it has two real solutions for y, it also has two real solutions for x, so there are two real solutions (intersections).

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