Zadanie 1.
I. Metoda podstawiania:
[tex]\left \{ {{x=9+y} \atop {x-5=2(y-5)}} \right. \\\left \{ {{x=9+y} \atop {9+y-5=2y-10}} \right. \\\left \{ {{x=9+y} \atop {y-2y=-10-9+5}} \right. \\\left \{ {{x=9+y} \atop {-y=-14 /*(-1)}} \right. \\\left \{ {{x=9+14} \atop {y=14}} \right. \\\left \{ {{x=23} \atop {y=14}} \right.[/tex]
II. Metoda przeciwnych współczynników:
[tex]\left \{ {{x=9+y} \atop {x-5=2(y-5)}} \right. \\\left \{ {{x-y=9} \atop {x-5=2y-10}} \right. \\\left \{ {{x-y=9 /*(-2)} \atop {x-2y=-10+5}} \right. \\\underline{+\left \{ {{-2x+2y=-18} \atop {x-2y=-5}} \right. }\\-2x+x=-18-5\\-x=-23 /*(-1)\\\bold{x=23}\\9+y=23 /-9\\\bold{y=14}[/tex]
Zadanie 2.
I. Metoda podstawiania:
[tex]\left \{ {{y-x=6} \atop {2x+2y=5x}} \right. \\\left \{ {{y=6+x} \atop {2x+2(6+x)=5x}} \right. \\\left \{ {{y=6+x} \atop {2x+12+2x=5x}} \right. \\\left \{ {{y=6+x} \atop {4x-5x=-12}} \right. \\\left \{ {{y=6+x} \atop {-x=-12 /*(-1)}} \right. \\\left \{ {{y=6+12} \atop {x=12}} \right. \\\left \{ {{y=18} \atop {x=12}} \right.[/tex]
II. Metoda przeciwnych współczynników:
[tex]\left \{ {{y-x=6} \atop {2x+2y=5x}} \right. \\\left \{ {{-x+y=6 /*(-3)} \atop {-3x+2y=0}} \right. \\\underline{+\left \{ {{3x-3y=-18} \atop {-3x+2y=0}} \right. }\\-3y+2y=-18\\-y=-18 /*(-1)\\\bold{y=18}\\18-x=6 /-18\\-x=-12 /*(-1)\\\bold{x=12}[/tex]
