Math Problem Solver

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

\[x = -1, y = -5\]\[x = 4, y = 5\]

Solve \(2 x - y = 3\) for \(x\). \[x = \frac{y}{2} + \frac{3}{2}\]Substitute \(\frac{y}{2} + \frac{3}{2}\) for \(x\) in \(x^{2} - x y = -4\) and simplify. $$\begin{aligned}x^{2} - x y &amp= -4 \\ \left(\frac{y}{2} + \frac{3}{2}\right)^{2} - \left(\frac{y}{2} + \frac{3}{2}\right) y &= -4 \\ y^{2} &= 25 \\ \sqrt{y^{2}} &= \sqrt{25} \\ y = -5&, y = 5\end{aligned}$$Substitute \(-5\) into \(2 x - y = 3\) to solve for \(x\). \[\begin{aligned}2 x + 5 &= 3\\2 x &= -2\\x &= -1\end{aligned}\]This yields the following solution. $$\begin{aligned}x = -1,\,y = -5\end{aligned}$$Substitute \(5\) into \(2 x - y = 3\) to solve for \(x\). \[\begin{aligned}2 x - 5 &= 3\\2 x &= 8\\x &= 4\end{aligned}\]This yields the following solution. $$\begin{aligned}x = 4,\,y = 5\end{aligned}$$