\(\displaystyle{x}={3}{y}^{{2}},{x}={y}^{{2}}+{7}\)

\(\displaystyle{3}{y}^{{2}}={y}^{{2}}+{7}\)

\(\displaystyle{2}{y}^{{2}}={7}\)

\(\displaystyle{y}^{{2}}=\frac{{7}}{{2}}\)

\(\displaystyle{y}=\pm\sqrt{{\frac{{7}}{{2}}}}\)

\(\displaystyle{y}=\sqrt{{\frac{{7}}{{2}}}}\)

\(\displaystyle{x}={3}\times\frac{{7}}{{2}}=\frac{{21}}{{2}}\)

or \(\displaystyle{y}=-\sqrt{{\frac{{7}}{{2}}}}\)

\(\displaystyle{x}=\frac{{21}}{{2}}\)

The points: \(\displaystyle{\left(\frac{{21}}{{2}},\sqrt{{\frac{{7}}{{2}}}}\right)},{\left(\frac{{21}}{{2}},-\sqrt{{\frac{{7}}{{2}}}}\right)}\).

\(\displaystyle{3}{y}^{{2}}={y}^{{2}}+{7}\)

\(\displaystyle{2}{y}^{{2}}={7}\)

\(\displaystyle{y}^{{2}}=\frac{{7}}{{2}}\)

\(\displaystyle{y}=\pm\sqrt{{\frac{{7}}{{2}}}}\)

\(\displaystyle{y}=\sqrt{{\frac{{7}}{{2}}}}\)

\(\displaystyle{x}={3}\times\frac{{7}}{{2}}=\frac{{21}}{{2}}\)

or \(\displaystyle{y}=-\sqrt{{\frac{{7}}{{2}}}}\)

\(\displaystyle{x}=\frac{{21}}{{2}}\)

The points: \(\displaystyle{\left(\frac{{21}}{{2}},\sqrt{{\frac{{7}}{{2}}}}\right)},{\left(\frac{{21}}{{2}},-\sqrt{{\frac{{7}}{{2}}}}\right)}\).