Verified answer

[tex]\displaystyle \left \{ {{\frac{x+3}{4}-\frac{y-2}{6}=1 } \atop {\frac{x-1}{8}+\frac{y+1}{6}=2 }} \right. \\\\\left \{ {{3x-2y=-1} \atop {3x+4y=47}} \right. \\\\\left \{ {{3x-2y=-1} \atop {-3x-4y=-47}} \right. \\\\-6y=-48\\y=8\\3x-2*8=-1\\x=5\\(x,y)=(5,8)[/tex]