Zad. 1
[tex]\left \{ {{\frac{x+y}2+x=2} \atop {\frac{x-y}2+y=1}} \right. \\\left \{ {{\frac{x+y}2+\frac{2x}2=2} \atop {\frac{x-y}2+\frac{2y}2=1}} \right. \\\left \{ {{\frac{x+y+2x}2=2} \atop {\frac{x-y+2y}2=1}} \right. \\\left \{ {{\frac{3x+y}2=2 /*2 \atop {\frac{x+y}2=1 /*2}} \right. \\\left \{ {{3x+y=4} \atop {x+y=2 /-y}} \right. \\\left \{ {{3(2-y)+y=4} \atop {x=2-y}} \right. \\\left \{ {{6-3y+y=4 /-6} \atop {x=2-y}} \right. \\[/tex]
[tex]\left \{ {{-2y=-2 /:(-2)} \atop {x=2-y}} \right. \\\left \{ {{y=1} \atop {x=1}} \right.[/tex]
Odp. A
Zad. 2
Z tresci zadania wynika, ze promienie obu okregow tworza z odcinkiem S1S2 trojkat rownoramienny o wierzcholkach S1, A, S2 lub S1, A, S2
[tex]|AB|=2h\\\frac12|S_1S_2|=a\\r=10\\a=\frac12*16=8\\\\a^2+h^2=r^2\\8^2+h^2=10^2\\64+h^2=100\\h^2=100-64\\h^2=36\\h=6\\2h=2*6=12\\|AB|=12\\\\Odp. C[/tex]
