[latex] left { {ig{6x-3x^2y^2-3=0} atop ig{-2x^3y+2y=0}} ight. \\ left { {ig{6x-3x^2y^2-3=0} atop ig{ycdot(-2x^3+2)=0}} ight. [/latex] Z drugiego równania wynika, że y=0 lub -2x³+2=0 [latex]1^o y=0\\ left { {ig{6x-3x^2cdot0^2-3=0} atop ig{y=0}qquadqquad} ight. \\ left { {ig{6x=3quad/:6} atop ig{y=0}quadqquad} ight.\\ left { {ig{x=frac12} atop ig{y=0}} ight.[/latex] [latex]\\\2^o -2x^3+2=0\\left { {ig{6x-3x^2y^2-3=0 } atop ig{-2x^3+2=0quad/:(-2)}} ight.\\left { {ig{6x-3x^2y^2-3=0} atop ig{x^3-1=0qquad}} ight.\\left { {ig{6x-3x^2y^2-3=0} atop ig{x^3=1qquad}} ight.\\left { {ig{6x-3x^2y^2-3=0} atop ig{x=1qquad}} ight.[/latex] [latex]left { {ig{6cdot1-3cdot1^2cdot y^2-3=0} atop ig{x=1qquad}} ight.\\left { {ig{3-3y^2=0quad/:(-3)} atop ig{x=1qquad}} ight.\\left { {ig{y^2-1=0} atop ig{x=1}} ight. \\left { {ig{(y+1)(y-1)=0} atop ig{x=1qquad}} ight.\\left { {ig{x=1} atop ig{y=1}} ight.qquadveeqquadleft { {ig{x=1 } atop ig{y=-1}} ight.[/latex] Czyli układ równań ma trzy rozwiązania: [latex]left { {ig{x=1} atop ig{y=1}} ight.qquadveeqquadleft { {ig{x=1 } atop ig{y=-1}} ight.qquadveeqquadleft { {ig{x=frac12} atop ig{y=0}} ight.[/latex]
