Answer
$(2,1)$ and $(5,4)$
Work Step by Step
$\left\{\begin{array}{l}{y=x-1}\\{y=x^{2}-6x+9}\end{array}\right.$
Graphed with desmos.com/calculator.
Substitute y into the second equation,
$\begin{aligned}x^{2}-6x+9&=x-1\\x^{2}-7x+10&=0\end{aligned}$
... two factors of 10 whose sum is -7 ... are -2 and -5.
$(x-2)(x-5)=0$
$\left[\begin{array}{ll}
x=2 & x=5\\
\text{... back -substitute} & \\
& \\
y=2-1 & y=5-1\\
y=1 & y=4\\
& \\
(2,1) & (5,4) \\
&
\end{array}\right]$
