xy=-25
y=x+10
You asked:
Solve the system of equations:\[\begin{aligned}x y &= -25\\y &= x + 10\end{aligned}\]
MathBot Answer:
The system of equations has one solution.
\[x = -5, y = 5\]
Solve \(x y = -25\) for \(x\). \[x = - \frac{25}{y}\]Substitute \(- \frac{25}{y}\) for \(x\) in \(y = x + 10\) and simplify. $$\begin{aligned}y &= x + 10 \\ y &= \left(- \frac{25}{y}\right) + 10 \\ y &= 10 - \frac{25}{y} \end{aligned}$$Substitute \(5\) into \(x y = -25\) to solve for \(x\). \[\begin{aligned}5 x &= -25\\x &= -5\end{aligned}\]This yields the following solution. $$\begin{aligned}x = -5,\,y = 5\end{aligned}$$