1) Metoda podstawiania:
[tex]\left \{ {{\frac{x}2-\frac{y}3=1/*6} \atop {x+2y=10 /-2y}} \right. \\\left \{ {{3x-2y=6} \atop {x=10-2y}} \right. \\\left \{ {{3(10-2y)-2y=6} \atop {x=10-2y}} \right. \\\left \{ {{30-6y-2y=6 /-30} \atop {x=10-2y}} \right. \\\left \{ {{-8y=6-30} \atop {x=10-2y}} \right. \\\left \{ {{-8y=-24 /:(-8)} \atop {x=10-2y}} \right. \\\left \{ {{y=3} \atop {x=10-2*3}} \right. \\\left \{ {{y=3} \atop {x=10-6}} \right. \\\left \{ {{y=3} \atop {x=4}} \right.[/tex]
2) Metoda przeciwnych wspolczynnikow:
[tex]\left \{ {{\frac{x}2-\frac{y}3=1 /*6} \atop {x+2y=10}} \right. \\+\left \{ {{3x-2y=6} \atop {x+2y=10}} \right. \\3x+x-2y+2y=6+10\\4x=16 /:4\\x=4\\4+2y=10 /-4\\2y=10-4\\2y=6 /:2\\y=3[/tex]
3) Metoda graficzna:
[tex]\frac{x}2-\frac{y}3=1\\0-\frac{y}3=1 /*3\\-y=3\\y=-3\\\frac{x}2-0=1 /*2\\x=2\\\left[\begin{array}{cc}x&y\\0&-3\\2&0\end{array}\right][/tex]
[tex]x+2y=10\\0+2y=10\\2y=10 /:2\\y=5\\\\x+0=10\\x=10\\\left[\begin{array}{cc}x&y\\0&5\\10&0\end{array}\right][/tex]
Uklad rownan w zalaczniku. Rozwiazaniem jest punkt P o wspolrzednych x=4; y=3
