Zad 1 {x + y = 2 {x - y = 4 ---------------------- 2x = 6 /:2 x = 3 x - y = 4 3 - y = 4 -y = 4 - 3 -y = 1 y = -1 {x = 3 {y = -1 Zad 2 {- 2x + 3y = -2 {3 (x - 1) + 2 (1- y) = 0 {- 2x + 3y = -2 {3x - 3 + 2 - 2y = 0 {- 2x + 3y = -2 {3x - 2y = 1 z drugiego 3x - 2y = 1 3x = 1 + 2y /:3 x = 1/3 + 2/3y - 2x + 3y = -2 -2*(1/3+2/3y) + 3y = -2 - 2/3 - 4/3y + 3y = -2 5/3y = - 1 1/3 = - 4/3 /*3/5 y = -4/5 x = 1/3 + 2/3y x = 1/3 + 2/3 * (-4/5) x = 1/3 - 8/15 = 5/15 - 8/15 x = -3/15 x = - 1/5 {x = - 1/5 {y = - 4/5
A. [latex] left { {{x+y=2} atop {x-y=4}} ight. [/latex] [latex]2x=6[/latex][latex]|:2[/latex] [latex]x=3[/latex] [latex]x+y=2[/latex] [latex]3+y=2[/latex] [latex]y=-1[/latex] [latex] left { {{x=3} atop {y=-1}} ight. [/latex] B. [latex] left { {{-2x+3y=-2} atop {3(x-1)+2(1-y)=0}} ight. [/latex] [latex] left { {{-2x+3y=-2} atop {3x-3+2-2y=0}} ight. [/latex] [latex] left { {{-2x+3y=-2|*3} atop {3x-2y=1|*2}} ight. [/latex] [latex] left { {{-6x+9y=-6} atop {6x-4y=2}} ight. [/latex] [latex]5y=-4|:5[/latex] [latex]y=- frac{4}{5} [/latex] [latex]-2x+3y=-2[/latex] [latex]-2x+3(- frac{4}{5} )=-2[/latex] [latex]-2x- frac{12}{5} =-2|*(-1)[/latex] [latex]2x+ frac{12}{5} =2[/latex] [latex]2x=2-2 frac{2}{5}[/latex] [latex]2x=- frac{2}{5}|:2[/latex] [latex]x=- frac{1}{5} [/latex] [latex] left { {x=- frac{1}{5} } atop {y=- frac{4}{5} }} ight. [/latex] Mam nadzieję, że nigdzie się nie pomyliłem, jeśli tak, proszę o kontakt.
