Math Problem Solver

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

\[D = 12, V = 16\]\[D = 16, V = 12\]

Solve \(D + V = 28\) for \(D\). \[D = 28 - V\]Substitute \(28 - V\) for \(D\) in \(D V = 192\) and simplify. $$\begin{aligned}D V &amp= 192 \\ \left(28 - V\right) V &= 192 \\ V^{2} - 28 V &= -192 \\V^{2} - 28 V + 192 &= 0 \\ \left(V - 16\right) \left(V - 12\right) &= 0 \\ V = 12&, V = 16\end{aligned}$$Substitute \(12\) into \(D + V = 28\) to solve for \(D\). \[\begin{aligned}D + 12 &= 28\\D &= 16\end{aligned}\]This yields the following solution. $$\begin{aligned}D = 16,\,V = 12\end{aligned}$$Substitute \(16\) into \(D + V = 28\) to solve for \(D\). \[\begin{aligned}D + 16 &= 28\\D &= 12\end{aligned}\]This yields the following solution. $$\begin{aligned}D = 12,\,V = 16\end{aligned}$$