Step 1

Given the system of equations.

\(\displaystyle-{2}{x}^{{2}}-{y}^{{2}}={200}\)...(1)

\(\displaystyle-{3}{x}^{{2}}-{y}^{{2}}={300}\)...(2)

Step 2

Subtracting equation (1) and (2)

\(\displaystyle-{2}{x}^{{2}}-{y}^{{2}}-{\left(-{3}{x}^{{2}}-{y}^{{2}}\right)}={200}-{300}\)

\(\displaystyle-{2}{x}^{{2}}-{y}^{{2}}+{3}{x}^{{2}}+{y}^{{2}}=-{100}\)

\(\displaystyle-{2}{x}^{{2}}+{3}{x}^{{2}}=-{100}\)

\(\displaystyle{x}^{{2}}=-{100}\)

\(\displaystyle{x}^{{2}}={\left({i}{10}\right)}^{{2}}\)

\(\displaystyle{x}=\pm{10}{i}\)

Putting the value \(\displaystyle{x}^{{2}}\) in equation (1)

\(\displaystyle-{2}{\left(-{100}\right)}-{y}^{{2}}={200}\)

\(\displaystyle{200}-{y}^{{2}}={200}\)

\(\displaystyle{y}^{{2}}={200}-{200}\)

\(\displaystyle{y}^{{2}}={0}\)

Solution of the given system is

x=-10i,10i and y = 0,0

Given the system of equations.

\(\displaystyle-{2}{x}^{{2}}-{y}^{{2}}={200}\)...(1)

\(\displaystyle-{3}{x}^{{2}}-{y}^{{2}}={300}\)...(2)

Step 2

Subtracting equation (1) and (2)

\(\displaystyle-{2}{x}^{{2}}-{y}^{{2}}-{\left(-{3}{x}^{{2}}-{y}^{{2}}\right)}={200}-{300}\)

\(\displaystyle-{2}{x}^{{2}}-{y}^{{2}}+{3}{x}^{{2}}+{y}^{{2}}=-{100}\)

\(\displaystyle-{2}{x}^{{2}}+{3}{x}^{{2}}=-{100}\)

\(\displaystyle{x}^{{2}}=-{100}\)

\(\displaystyle{x}^{{2}}={\left({i}{10}\right)}^{{2}}\)

\(\displaystyle{x}=\pm{10}{i}\)

Putting the value \(\displaystyle{x}^{{2}}\) in equation (1)

\(\displaystyle-{2}{\left(-{100}\right)}-{y}^{{2}}={200}\)

\(\displaystyle{200}-{y}^{{2}}={200}\)

\(\displaystyle{y}^{{2}}={200}-{200}\)

\(\displaystyle{y}^{{2}}={0}\)

Solution of the given system is

x=-10i,10i and y = 0,0