x(-2-3y)=0
y(3-y)=0
You asked:
Solve the system of equations:\[\begin{aligned}x\left( -2 - 3 y \right) &= 0\\y\left( 3 - y \right) &= 0\end{aligned}\]
MathBot Answer:
The system of equations has \(2\) solutions.
\[x = 0, y = 0\]\[x = 0, y = 3\]
Solve \(y \left(3 - y\right) = 0\) for \(y\). $$\begin{aligned}y \left(3 - y\right) &= 0\\y \left(3 - y\right) &= 0 \\ - y \left(y - 3\right) &= 0 \\ y = 0&, y = 3\end{aligned}$$Substitute \(0\) for \(y\) in \(x \left(- 3 y - 2\right) = 0\) and solve.\[\begin{aligned}- 2 x &= 0\\x &= 0\end{aligned}\]This yields the following solutions. $$\begin{aligned}x = 0,\,y = 3\\ x = 0,\,y = 0\end{aligned}$$