\left \{ {{x-y=-1 } \atop {-x+2y=-3}} \right.
\left \{ {{x=-1+y } \atop {-(-1+y)+2y=-3}} \right.
\left \{ {{x=-1+y } \atop {1-y+2y=-3}} \right.
\left \{ {{x=-1+y } \atop {1+y=-3}} \right.
\left \{ {{x=-1+y } \atop {y=-3-1}} \right.
\left \{ {{x=-1+y } \atop {y=-4}} \right.
\left \{ {{x=-1+(-4) } \atop {y=-4}} \right.
\left \{ {{x=-1-4 } \atop {y=-4}} \right.
\left \{ {{x=-5 } \atop {y=-4}} \right.
…
\left \{ {{x+4y=6 } \atop {4x+y=-6}} \right.
\left \{ {{x=6-4y } \atop {4(6-4y )+y=-6}} \right.
\left \{ {{x=6-4y } \atop {24-16y +y=-6}} \right.
\left \{ {{x=6-4y } \atop {24-15y=-6}} \right.
\left \{ {{x=6-4y } \atop {-15y=-6-24}} \right.
\left \{ {{x=6-4y } \atop {-15y=-30}} \right.
\left \{ {{x=6-4y } \atop {y=2}} \right.
\left \{ {{x=6-4*2 } \atop {y=2}} \right.
\left \{ {{x=6-8 } \atop {y=2}} \right.
\left \{ {{x=-2 } \atop {y=2}} \right.
…
\left \{ {{2x+2y=6 } \atop {4x-y=7}} \right.
\left \{ {{x+y=3 } \atop {4x-y=7}} \right.
\left \{ {{x=3-y } \atop {4(3-y)-y=7}} \right.
\left \{ {{x=3-y } \atop {12-4y-y=7}} \right.
\left \{ {{x=3-y } \atop {12-5y=7}} \right.
\left \{ {{x=3-y } \atop {-5y=7-12}} \right.
\left \{ {{x=3-y } \atop {-5y=-5}} \right.
\left \{ {{x=3-y } \atop {y=1}} \right.
\left \{ {{x=3-1 } \atop {y=1}} \right.
\left \{ {{x=2 } \atop {y=1}} \right.