1).Metoda podstawiania a). {x+y=3 {x-2y=6 {x=3-y {3-y-2y=6 {x=3-y {-3y=6-3 {x=3-y {-3y=3 /:(-3) {x=3-y {y= -1 {x=3-(-1) {y= -1 {x=3+1 {y= -1 {x=4 {y= -1 b). {x-y=5 {3x+4y=8 {x=5+y {3·(5+y)+4y=8 {x=5+y {15+3y+4y=8 {x=5+y {7y=8-15 {x=5+y {7y= -7 /:7 {x=5+y {y= -1 {x=5-1 {y= -1 {x=4 {y= -1 2. Metoda przeciwnych współczynnikow a). {x+y=5 + {x-y=1 ----------- 2x=6 /:2 x=3 x+y=5 3+y=5 y=5-3 y=2 {x=3 {y=2 b). {2x-y=4 + {-x+y= -7 ------------ x= -3 2x-y=4 2·(-3)-y=4 -6-y=4 -y=4+6 -y=10 /·(-1) y= -10 {x= -3 {y= -10
Zadanie 1. (metoda podstawiania) a) {x + y = 3 {x - 2y = 6 x = 6 + 2y {x = 6 + 2y {6 + 2y + y = 3 {x = 6 + 2y {6 + 3y = 3 {x = 6 + 2y {3y = 3 - 6 {3y = -3 {y = (-1) x + y = 3 x + (-1) = 3 x - 1 = 3 x = 3 + 1 x = 4 {x = 4 {y = (-1) ——————————————————————————————— b) {x - y = 5 {3x + 4y = 8 {x = 5 + y {3x + 4y = 8 {x = 5 + y {3(5 + y) + 4y = 8 {x = 5 + y {15 + 3y + 4y = 8 {x = 5 + y {15 + 7y = 8 {x = 5 + y {7y = 8 - 15 7y = 8 - 15 7y = -7 y = (-1) x - y = 5 x - (-1) = 5 x + 1 = 5 x = 4 {x = 4 {y = (-1) ——————————————————————————————————————————— Zadanie 2. (metoda przeciwnych współczynników) a) {x + y = 5 +{x - y = 1 ———— 2x = 6 x = 3 x + y = 5 3 + y = 5 y = 2 {x = 3 {y = 2 ——————————————————————————— b) {2x - y = 4 +{-x + y = -7 —————— x = (-3) 2x - y = 4 2*(-3) - y = 4 -6 - y = 4 -y = 4 + 6 -y = 10 y = (-10) {x = (-3) {y = (-10) Pozdrawiam, Bartek
