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.