xy=-16
y=x+8
You asked:
Solve the system of equations:\[\begin{aligned}x y &= -16\\y &= x + 8\end{aligned}\]
MathBot Answer:
The system of equations has one solution.
\[x = -4, y = 4\]
Solve \(x y = -16\) for \(x\). \[x = - \frac{16}{y}\]Substitute \(- \frac{16}{y}\) for \(x\) in \(y = x + 8\) and simplify. $$\begin{aligned}y &= x + 8 \\ y &= \left(- \frac{16}{y}\right) + 8 \\ y &= 8 - \frac{16}{y} \end{aligned}$$Substitute \(4\) into \(x y = -16\) to solve for \(x\). \[\begin{aligned}4 x &= -16\\x &= -4\end{aligned}\]This yields the following solution. $$\begin{aligned}x = -4,\,y = 4\end{aligned}$$