Math Problem Solver

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

\[x = 2, y = 4\]\[x = 4, y = 2\]

Solve \(x + y = 6\) for \(x\). \[x = 6 - y\]Substitute \(6 - y\) for \(x\) in \(x y = 8\) and simplify. $$\begin{aligned}x y &amp= 8 \\ \left(6 - y\right) y &= 8 \\ y^{2} - 6 y &= -8 \\y^{2} - 6 y + 8 &= 0 \\ \left(y - 4\right) \left(y - 2\right) &= 0 \\ y = 2&, y = 4\end{aligned}$$Substitute \(2\) into \(x + y = 6\) to solve for \(x\). \[\begin{aligned}x + 2 &= 6\\x &= 4\end{aligned}\]This yields the following solution. $$\begin{aligned}x = 4,\,y = 2\end{aligned}$$Substitute \(4\) into \(x + y = 6\) to solve for \(x\). \[\begin{aligned}x + 4 &= 6\\x &= 2\end{aligned}\]This yields the following solution. $$\begin{aligned}x = 2,\,y = 4\end{aligned}$$