Verified answer

[tex]\displaystyle\bf\\\left \{ {{2x+9y=2} \ |\cdot(-4) \atop {8x-15y=9}} \right. \\\\\\+\left \{ {{-8x-36y=-8} \atop {8x-15y=9}} \right. \\-----------\\-51y=1\\\\y=-\frac{1}{51} \\\\2x=2-9y=2-9\cdot\bigg(-\frac{1}{51} \bigg)=2+\frac{9}{51} =2\frac{3}{17} \\\\\\x=2\frac{3}{17} :2=\frac{37}{17} \cdot\frac{1}{2} =\frac{37}{34} =1\frac{3}{34} \\\\\\Otvet: \ \bigg(1\frac{3}{34} \ ; \ -\frac{1}{51} \bigg)[/tex]