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Solve the system by x² 3x y=0 2x y=5.

1 Answer

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Final answer:

To solve the system of equations x² + 3xy = 0 and 2xy = 5, we can use substitution. Solving for y, we find that there are no real solutions for y. Therefore, the system of equations has no solution.

Step-by-step explanation:

To solve the system of equations:

x^2 + 3xy = 0

2xy = 5

We can solve this system by substitution.

  • First, solve the second equation for x:
  • 2xy = 5
  • x = 5/(2y)
  • Now substitute this value of x into the first equation:
  • (5/(2y))^2 + 3(5/(2y))y = 0
  • 25/(4y^2) + (15y/2y) = 0
  • 25/(4y^2) + 15/2 = 0
  • 25 + 30y^2 = 0
  • 30y^2 = -25
  • y^2 = -25/30
  • y^2 = -5/6
  • y = ±√(-5/6)
  • y = ±(√5/i√6)
  • y = ±(√5/√6)i
  • Therefore, there are no real solutions for y.

So, the system of equations has no solution.

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