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

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

Question
Equations
asked 2020-11-30
Solve the following system of Equations.
\(\displaystyle-{2}{x}^{{2}}-{y}^{{2}}=-{200}\)
\(\displaystyle-{3}{x}^{{2}}-{y}^{{2}}=-{300}\)

Answers (1)

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
0

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