Verified answer

[tex]\displaystyle\\\left \{ {{\frac{x}{3} -\frac{y}{2} +3=0|\times6} \atop {\frac{x}{2} +\frac{y}{5} -5}=0|\times10} \right. \\\\\left \{ {{2x-3y+18=0} \atop {5x+2y-5=0}} \right. \\\\\left \{ {{x=\frac{-18+3y}{2}} \atop {5x+2y-5=0}} \right. \\\\\frac{5(-18+3y)}{2}+2y-5=0|\times2\\ 5(-18+3y)+4y-10=0\\15y+4y-90-10=0\\19y=100\\y=\frac{100}{19}= > \\ \\x=\frac{-18+3\times\frac{100}{19}}{2} \\\\x=\frac{-18+15\frac{15}{19}}{2} \\\\x=\frac{-\frac{42}{19} }{2} =-\frac{84}{19}[/tex]