2xy-3x^2=50
y-x^3+6x=0
You asked:
Solve the system of equations:\[\begin{aligned}2 x y - 3 {x}^{2} &= 50\\y - {x}^{3} + 6 x &= 0\end{aligned}\]
MathBot Answer:
The system of equations has \(4\) solutions.
\[x = \sqrt{10}, y = 4 \sqrt{10}\]\[x = - \sqrt{10}, y = - 4 \sqrt{10}\]\[x = - \frac{\sqrt{10} i}{2}, y = \frac{17 \sqrt{10} i}{4}\]\[x = \frac{\sqrt{10} i}{2}, y = - \frac{17 \sqrt{10} i}{4}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).