x=ecos²t
y=esin²t
You asked:
Solve the system of equations:\[\begin{aligned}x &= e \cdot {\cos\left( t \right)}^{2}\\y &= e \cdot {\sin\left( t \right)}^{2}\end{aligned}\]
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}x &= e \cos^{2}{\left(t \right)}\\y &= e \sin^{2}{\left(t \right)}\end{aligned}$$\(t\) is a free variable.