Math Problem Solver

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

\[x = 84, y = \frac{230}{3}\]\[x = 92, y = 70\]

Solve \(x y = 6440\) for \(x\). \[x = \frac{6440}{y}\]Substitute \(\frac{6440}{y}\) for \(x\) in \(5 x + 6 y = 880\) and simplify. $$\begin{aligned}5 x + 6 y &amp= 880 \\ 5 \left(\frac{6440}{y}\right) + 6 y &= 880 \\ 6 y + \frac{32200}{y} &= 880 \end{aligned}$$Substitute \(70\) into \(x y = 6440\) to solve for \(x\). \[\begin{aligned}70 x &= 6440\\x &= 92\end{aligned}\]This yields the following solution. $$\begin{aligned}x = 92,\,y = 70\end{aligned}$$Substitute \(\frac{230}{3}\) into \(x y = 6440\) to solve for \(x\). \[\begin{aligned}\frac{230 x}{3} &= 6440\\x &= 84\end{aligned}\]This yields the following solution. $$\begin{aligned}x = 84,\,y = \frac{230}{3}\end{aligned}$$