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