`1`

   $\left \{ {{x+2y=12} \atop {3x-y=1}} \right.$  

   $\left \{ {{x=12-2y} \atop {3(12-2y)-y=1}} \right.$ 

   $\left \{ {{x=12-2y} \atop {36-6y-y=1}} \right.$ 

   $\left \{ {{x=12-2y} \atop {-7y=1-36}} \right.$ 

   $\left \{ {{x=12-2y} \atop {-7y=-35}} \right.$ 

   $\left \{ {{x=12-2y} \atop {y=5}} \right.$ 

   $\left \{ {{x=12-2.5} \atop {y=5}} \right.$ 

   $\left \{ {{x=2} \atop {y=5}} \right.$ 

`2`

   $\left \{ {{-12x-3y=12} \atop {4x+3y=-6}} \right.$ 

   $\left \{ {{-8x=6} \atop {4x+3y=-6}} \right.$ 

   $\left \{ {{x=\frac{3}{-4}} \atop {4.\frac{3}{-4}+3y=-6}} \right.$ 

   $\left \{ {{x=\frac{3}{-4}} \atop {-3+3y=-6}} \right.$ 

   $\left \{ {{x=\frac{3}{-4}} \atop {3y=-3}} \right.$ 

   $\left \{ {{x=\frac{3}{-4}} \atop {y=-1}} \right.$ 

`3`

    $\left \{ {{2x+y=7} \atop {5x-4y=-2}} \right.$   

    $\left \{ {{y=7-2x} \atop {5x-4(7-2x)=-2}} \right.$   

    $\left \{ {{y=7-2x} \atop {5x-28+8x=-2}} \right.$   

    $\left \{ {{y=7-2x} \atop {13x-28=-2}} \right.$     

    $\left \{ {{y=7-2x} \atop {13x=26}} \right.$ 

    $\left \{ {{y=7-2x} \atop {x=2}} \right.$   

   $\left \{ {{y=7-2.2} \atop {x=2}} \right.$ 

   $\left \{ {{y=3} \atop {x=2}} \right.$ 

`4`

   $\left \{ {{x-2y=5} \atop {2x+3y=3}} \right.$ 

   $\left \{ {{x=5+2y} \atop {2(5+2y)+3y=3}} \right.$ 

   $\left \{ {{x=5+2y} \atop {10+4y+3y=3}} \right.$ 

   $\left \{ {{x=5+2y} \atop {7y=3-10}} \right.$ 

   $\left \{ {{x=5+2y} \atop {7y=-7}} \right.$ 

   $\left \{ {{x=5+2y} \atop {y=-1}} \right.$ 

   $\left \{ {{x=5+2.-1} \atop {y=-1}} \right.$ 

   $\left \{ {{x=3} \atop {y=-1}} \right.$