Math Problem Solver

The system of equations has \(2\) solutions.

\[x = 0, y = 1\]\[x = \frac{2}{3}, y = 3\]

Solve \(3 x - y - 3 = -4\) for \(x\). \[x = \frac{y}{3} - \frac{1}{3}\]Substitute \(\frac{y}{3} - \frac{1}{3}\) for \(x\) in \(x y - y = -1\) and simplify. $$\begin{aligned}x y - y &= -1 \\ \left(\frac{y}{3} - \frac{1}{3}\right) y - y &= -1 \\ y^{2} - 4 y &= -3 \\y^{2} - 4 y + 3 &= 0 \\ \left(y - 3\right) \left(y - 1\right) &= 0 \\ y = 1&, y = 3\end{aligned}$$Substitute \(1\) into \(3 x - y - 3 = -4\) to solve for \(x\). \[\begin{aligned}3 x - 4 &= -4\\3 x &= 0\\x &= 0\end{aligned}\]This yields the following solution. $$\begin{aligned}x = 0,\,y = 1\end{aligned}$$Substitute \(3\) into \(3 x - y - 3 = -4\) to solve for \(x\). \[\begin{aligned}3 x - 6 &= -4\\3 x &= 2\\x &= \frac{2}{3}\end{aligned}\]This yields the following solution. $$\begin{aligned}x = \frac{2}{3},\,y = 3\end{aligned}$$