2x + 9y= -9=>x=(-9-9y)/2 -3(-9-9y)/2+3y= 8/*2 27+27y+6y=16 33y=-11/33 y=-⅓ x=(-9+9*1/3)/2=-3 x - y = 0=>x=y x + y +z =4 x + 2y +3z = 9 x=y 2x+z=4=>z=4-2x x+2x+3(4-2x)=9 -3x=-3/(-3) x=1 y=1 z=4-2=2 -2x + y = 0/*3=>-6x+3y=0 sumujemy oba 3x - 3y =1 -3x=1/(-3) x=-⅓ -⅓*3 -3y=1 -3y=2/(-3) y=-2/3
Układy równań metoda podstawiania: 1. 2x + 9y = -9 -3x+3y = 8 2x + 9y = - 9 3y = 8 + 3x 2x + 3(8 + 3x) = - 9 3y = 8 + 3x 2x + 24 + 9x = - 9 3y = 8 + 3x 11x = -33 3y = 8 + 3x x = - 3 3y = 8 + 3x x = - 3 3y = 8 + 3( -3) x = - 3 3y = 8 – 9 x = - 3 3y = -1 x = - 3 y = -1/3 2. x - y = 0 x + y +z =4 x + 2y +3z = 9 x = y z = 4 – x – y x + 2y +3z = 9 x = y z = 4 – x – y y + 2y + 3(4 – y – y) = 9 x = y z = 4 – x – y 3y + 12 – 6y = 9 x = y z = 4 – x – y -3y = -3 x = 1 z = 4 – 1 – 1 y = 1 x = 1 z = 2 y = 1 Metodą przeciwnych współczynników: 1. -2x + y = 0 3x - 3y =1 -6x + 3y = 0 3x – 3y = 1 - 3x = 1 3x = -1 x = -1/3 y = 2x y = - 2/3 x = -1/3 y = - 2/3
