# Solve the following system of Equations. -2x^2-y^2=-200 -3x^2-y^2=-300

Question
Equations
Solve the following system of Equations.
$$\displaystyle-{2}{x}^{{2}}-{y}^{{2}}=-{200}$$
$$\displaystyle-{3}{x}^{{2}}-{y}^{{2}}=-{300}$$

2020-12-01
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

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$$\displaystyle{\left({x}_{{{1}}},{x}_{{{2}}},{x}_{{{3}}}\right)}=$$