Math Problem Solver

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

\[a = -20, b = -64\]\[a = 64, b = 20\]

Solve \(a - b = 44\) for \(a\). \[a = b + 44\]Substitute \(b + 44\) for \(a\) in \(a b = 1280\) and simplify. $$\begin{aligned}a b &amp= 1280 \\ \left(b + 44\right) b &= 1280 \\ b^{2} + 44 b &= 1280 \\b^{2} + 44 b - 1280 &= 0 \\ \left(b - 20\right) \left(b + 64\right) &= 0 \\ b = -64&, b = 20\end{aligned}$$Substitute \(-64\) into \(a - b = 44\) to solve for \(a\). \[\begin{aligned}a + 64 &= 44\\a &= -20\end{aligned}\]This yields the following solution. $$\begin{aligned}a = -20,\,b = -64\end{aligned}$$Substitute \(20\) into \(a - b = 44\) to solve for \(a\). \[\begin{aligned}a - 20 &= 44\\a &= 64\end{aligned}\]This yields the following solution. $$\begin{aligned}a = 64,\,b = 20\end{aligned}$$