Question

How many real solutions intersections weather be in the system of two equations

Answer 1

• Two real solutions

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Given is the system of equations.

Solve it by substitution, y² = x² + 16

• 5x² + y² = 30
• 5x² + x² + 16 = 30
• 6x² = 14
• x² = 14/6
• x² = 7/3
• x = ±
  `√(7/3)`

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