Math Problem Solver

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

\[x = 3, y = 4\]\[x = 4, y = 3\]

Solve \(x + y = 7\) for \(x\). \[x = 7 - y\]Substitute \(7 - y\) for \(x\) in \(x y = 12\) and simplify. $$\begin{aligned}x y &amp= 12 \\ \left(7 - y\right) y &= 12 \\ y^{2} - 7 y &= -12 \\y^{2} - 7 y + 12 &= 0 \\ \left(y - 4\right) \left(y - 3\right) &= 0 \\ y = 3&, y = 4\end{aligned}$$Substitute \(3\) into \(x + y = 7\) to solve for \(x\). \[\begin{aligned}x + 3 &= 7\\x &= 4\end{aligned}\]This yields the following solution. $$\begin{aligned}x = 4,\,y = 3\end{aligned}$$Substitute \(4\) into \(x + y = 7\) to solve for \(x\). \[\begin{aligned}x + 4 &= 7\\x &= 3\end{aligned}\]This yields the following solution. $$\begin{aligned}x = 3,\,y = 4\end{aligned}$$