Rozwiazanie metoda podstawiania:
[tex]\left \{ {{4x-5y=9 /+5y} \atop {-5x+2y=-31}} \right. \\\left \{ {{4x=9+5y /:4} \atop {-5x+2y=-31}} \right. \\\left \{ {{x=\frac{9+5y}4} \atop {-5x+2y=-31}} \right. \\-5*\frac{9+5y}4+2y=-31\\\frac{-5(9+5y)}4+2y=-31\\\frac{-45-25y}4+2y=-31 /*4\\-45-25y+8y=-124/+45\\-17y=-79 /:(-17)\\y=\frac{79}{17}\\4x-5*\frac{79}{17}=9\\4x-\frac{395}{17}=9 /+\frac{395}{17}\\4x=\frac{153}{17}+\frac{395}{17}\\4x=\frac{548}{17} /*\frac14\\x=\frac{548}{17}*\frac14\\x=\frac{137}{17}[/tex]
Rozwiazanie metoda przeciwnych wspolczynnikow:
[tex]\left \{ {{4x-5y=9/*5} \atop {-5x+2y=-31/*4}} \right. \\+\left \{ {{20x-25y=45} \atop {-20x+8y=-124}} \right. \\-25y+8y=45-124\\-17y=-79 /:(-17)\\y=\frac{79}{17}\\\left \{ {{4x-5y=9/*2} \atop {-5x+2y=-31/*5}} \right. \\+\left \{ {{8x-10y=18} \atop {-25x+10y=-155}} \right. \\8x-25x=18-155\\-17x=-137 /:(-17)\\x=\frac{137}{17}[/tex]
