Answer
$(0,1)$ and $(4,17)$
Work Step by Step
$\left\{\begin{array}{l}{y=x^{2}+1}\\{y=4x+1}\end{array}\right.$
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Subtracting the equations,
$0=x^{2}+1-4x-1$
$0=x^{2}-4x$
$0=x(x-4)$
$\left[\begin{array}{lll}
& x=0 & x=4\\
\text{back-substitute:} & y=4(0)+1 & y=4(4)+1\\
& y=1 & y-2\\
& & \\
& (0,1) & (4,17)\\
& &
\end{array}\right]$