Verified answer

[tex]\displaystyle\bf\\\left \{ {{2x+y=3} \atop {x^{2} +2xy+3y^{2}=3 }} \right. \\\\\\\left \{ {{y=3-2x} \atop {x^{2} +2x\cdot(3-2x)+3\cdot(3-2x)^{2}=3 }} \right. \\\\\\\left \{ {{y=3-2x} \atop {x^{2} +6x-4x^{2} +27-36x+12x^{2} =3}} \right. \\\\\\\left \{ {{y=3-2x} \atop {9x^{2} -30x+24=0}} \right. \\\\\\\left \{ {{y=3-2x} \atop {3x^{2} -10x+8=0}} \right. \\\\\\3x^{2} -10x+8=0\\\\D=(-10)^{2} -4\cdot 3\cdot 8=100-96=4=2^{2} \\\\\\x_{1} =\frac{10-2}{6} =\frac{8}{6}=1\frac{1}{3}[/tex]

[tex]\displaystyle\bf\\x_{2} =\frac{10+2}{6} =\frac{12}{6} =2\\\\\\y_{1} =3-2\cdot \frac{4}{3} =3-\frac{8}{3} =3-2\frac{2}{3} =\frac{1}{3} \\\\\\y_{2} =3-2\cdot 2=3-4=-1\\\\\\Otvet \ : \ \Big(1\frac{1}{3} \ ; \ \frac{1}{3} \Big) \ \ , \ \ \Big(2 \ ; \ -1\Big)[/tex]