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Question Number 151115 by mathdanisur last updated on 18/Aug/21

$$\mathrm{Solve}\mathrm{the}\mathrm{system}:$$$$\{\begin{array}{l}{\mathrm{x}}^2{\mathrm{y}}^2+{\mathrm{xy}}^2+\mathrm{x}+\mathrm{y}=0\\ {\mathrm{x}}^2\mathrm{y}+\mathrm{xy}+1=0\end{array}$$

Answered by dumitrel last updated on 18/Aug/21

$$y(x^{2}y+xy+1)+x=0\Rightarrow y\cdot 0+x=0\Rightarrow x=0$$$$\Rightarrow 0+0+1=0\Rightarrow nosolution$$

Commented by mathdanisur last updated on 18/Aug/21

$$\mathrm{Thank}\mathrm{You}\mathbf{S}\mathrm{er}$$

Answered by Rasheed.Sindhi last updated on 18/Aug/21

$$\{\begin{array}{l}{\mathrm{x}}^2{\mathrm{y}}^2+{\mathrm{xy}}^2+\mathrm{x}+\mathrm{y}=0\\ ({\mathrm{x}}^2\mathrm{y}+\mathrm{xy}+1=0)\times \mathrm{y}\end{array}$$$$\{\begin{array}{l}{\mathrm{x}}^2{\mathrm{y}}^2+{\mathrm{xy}}^2+\mathrm{x}+\mathrm{y}=0.....\left(\mathrm{i}\right)\\ {\mathrm{x}}^2{\mathrm{y}}^2+{\mathrm{xy}}^2+\mathrm{y}=0..........\left(\mathrm{ii}\right)\end{array}$$$$\left(\mathrm{i}\right)-\left(\mathrm{ii}\right):\mathrm{x}=0$$$$This{doesn}^{\prime }tsatisfythesecond$$$$givenequation\to Nosolution$$

Commented by mathdanisur last updated on 18/Aug/21

$$\mathrm{Thank}\mathrm{You}\mathrm{Ser}$$

Answered by Olaf_Thorendsen last updated on 18/Aug/21

$$\mathrm{in}\mathbb{C},x=e^{i\frac{2\pi }{3}},y=2\mathrm{or}{e}^{i\frac{4\pi }{3}},y=2$$

Commented by MJS_new last updated on 18/Aug/21

$$\mathrm{how}?$$

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