Verified answer

[tex]\displaystyle\bf\\\left \{ {{\dfrac{5}{6} x+\dfrac{1}{3} y=\dfrac{-1}{3} } \atop {x+\dfrac{2}{3} y=\dfrac{2}{3} }} \right. \\\\\\\left \{ {{\dfrac{5}{6} x\cdot 6+\dfrac{1}{3} y\cdot 6=\dfrac{-1}{3} \cdot 6} \atop {x\cdot 3+\dfrac{2}{3} y\cdot 3=\dfrac{2}{3} \cdot 3}} \right. \\\\\\\left \{ {{5x+2y=-2} \atop {3x+2y=2}} \right. \\\\\\\left \{ {{2y=2-3x} \atop {5x+2-3x=-2}} \right. \\\\\\\left \{ {{2y=2-3x} \atop {2x=-4}} \right. \\\\\\\left \{ {{x=-2} \atop {2y=2-3\cdot(-2)}} \right.[/tex]

[tex]\displaystyle\bf\\\left \{ {{x=-2} \atop {2y=2+6}} \right. \\\\\\\left \{ {{x=-2} \atop {2y=8}} \right.\\\\\\\left \{ {{x=-2} \atop {y=4}} \right. \\\\\\Otvet: \Big (-2 \ ; \ 4\Big)[/tex]