Math Problem Solver

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

\[a = 9, b = 8\]\[a = 13, b = 4\]

Solve \(a + b = 17\) for \(a\). \[a = 17 - b\]Substitute \(17 - b\) for \(a\) in \(a b - 5 b = 32\) and simplify. $$\begin{aligned}a b - 5 b &amp= 32 \\ \left(17 - b\right) b - 5 b &= 32 \\ b^{2} - 12 b &= -32 \\b^{2} - 12 b + 32 &= 0 \\ \left(b - 8\right) \left(b - 4\right) &= 0 \\ b = 4&, b = 8\end{aligned}$$Substitute \(4\) into \(a + b = 17\) to solve for \(a\). \[\begin{aligned}a + 4 &= 17\\a &= 13\end{aligned}\]This yields the following solution. $$\begin{aligned}a = 13,\,b = 4\end{aligned}$$Substitute \(8\) into \(a + b = 17\) to solve for \(a\). \[\begin{aligned}a + 8 &= 17\\a &= 9\end{aligned}\]This yields the following solution. $$\begin{aligned}a = 9,\,b = 8\end{aligned}$$