Step 1

1) \(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={10}\)

2) \(\displaystyle{9}{x}^{{{2}}}+{y}^{{{2}}}={18}\)

Subtracting (1) from (2)

\(\displaystyle-{8}{x}^{{{2}}}=-{8}\)

\(\displaystyle{x}^{{{2}}}=-{1}\)

\(\displaystyle{x}=\pm{1}\)

Putting the value of x in (1)

\(\displaystyle{\left(\pm{1}\right)}^{{{2}}}+{y}^{{{2}}}={10}\)

\(\displaystyle{y}^{{{2}}}={10}-{1}\)

\(\displaystyle{y}^{{{2}}}={9}\)

\(\displaystyle{y}=\pm{3}\)

1) \(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={10}\)

2) \(\displaystyle{9}{x}^{{{2}}}+{y}^{{{2}}}={18}\)

Subtracting (1) from (2)

\(\displaystyle-{8}{x}^{{{2}}}=-{8}\)

\(\displaystyle{x}^{{{2}}}=-{1}\)

\(\displaystyle{x}=\pm{1}\)

Putting the value of x in (1)

\(\displaystyle{\left(\pm{1}\right)}^{{{2}}}+{y}^{{{2}}}={10}\)

\(\displaystyle{y}^{{{2}}}={10}-{1}\)

\(\displaystyle{y}^{{{2}}}={9}\)

\(\displaystyle{y}=\pm{3}\)