[tex]\displaystyle \left \{ {{x+y=8} \atop {x-y=2}} \right. \\x+x+y-y=8+2\\2x=10\\x=5= > y=3[/tex]

[tex]\displaystyle\left \{ {{x-y=3|\times(-2)} \atop {2x+3y=1}} \right. \\\\\displaystyle\left \{ {{-2x+2y=-6} \atop {2x+3y=1}} \right.\\2x-2x+2y+3y=-6+1\\5y=-5\\y=-1= > x=2[/tex]

[tex]\displaystyle\left \{ {{\dfrac{2x+1}{5} =\dfrac{y-1}{2} } \atop {4x+5y=23}} \right. \\\\\left \{ {{2(2x+1)=5(y-1)} \atop {4x+5y=23}} \right. \\\\\left \{ {{4x+2=5y-5} \atop {4x+5y=23}} \right. \\\\\left \{ {{4x-5y=-7} \atop {4x+5y=23}} \right. \\\\4x+4x-5y+5y=23-7\\8x=16\\x=2= > y=3[/tex]