Metoda algebraiczna ma 3 wersje: 1. metoda podstawiania 2. metoda przeciwnych wqspółczynników 3. metoda wyznaczników zadania poniższe są rozwiazane metodą drugą i pierwszą a) metoda prezeciwnych współczynników 7x-3y =15 /*2 5x+6y=27 14x -6y = 30 | + 5x + 6y = 27 | ----------------------- 19x = 57 x = 57:19 x = 3 5*3 + 6y = 27 6y = 27 -15 6y = 12 y = 12 : 6 y = 2 x = 3 y = 2 b) 7x-3y+1=0 4x-5y+17=0 7x -3y = -1 /*5 4x -5y = -17 /*(-3) 35x - 15y = -5 | -12x + 15y = 51 | + ---------------------- 23x = 46 x = 46 : 23 x = 2 4*2 -5y = -17 -5y = -17 -8 y = (-25): (-5) y = 5 x = 2 y = 5 c) metoda podstawiania 3x+5y=4 7x-3y=2 3x = 4 -5y 7x -3y = 2 x = 1/3(4 -5y) 7*1/3(4 -5y) -3y = 2 x = 1/3(4 -5y) 28/3 - (35/3)y -3y = 2 x = 1/3(4 -5y) ( -35/3)y - (9/3)y = 6/3 - 28/3 x = 1/3(4 -5y) (- 44/3)y = (- 22/3) x = 1/3(4 -5y) y = (-22/3):(-44/3) x = 1/3(4 -5y) y = (-22/3)*(-3/44) x = 1/3(4 -5y) y = 1/2 x = 1/3( 4 - 5*1/2) = 1/3( 8/2-5/2)= 1/3*(3/2)= 1/2 y = 1/2 x = 1/2 y = 1/2 d) x-7y=3 5x-21y=11 x = 3 + 7y 5*(3 + 7y) - 21y = 11 x = 3 + 7y 15 + 35y -21y = 11 x = 3 + 7y 14y = 11-15 x = 3 + 7y y = (-4) : 14 x = 3 + 7y y = - 2/7 x = 3 + 7*(-2/7)= 3 - 2 = 1 y = -2/7 x = 1 y = -2/7 e) -8x+3y=15 7x-2y=0 -8x + 3y = 15 -2y = -7x -8x + 3y = 15 y = -7x : (-2) -8x + 3y = 15 y = (7/2)x -8x + 3(7/2x) = 15 y = 7/2x - 16/2x + 21/2x = 15 y = 7/2x 5/2x = 15 y = 7/2x x = 15 : (5/2) y = 7/2 x x = 15*(2/5) y = 7/2x x = 6 y = 7/2*6 = 21 x = 6 y = 21 f) 2x+y=4 x-2y=7 y = 4 -2x x -2(4 -2x) = 7 y = 4 -2x x - 8 + 4x = 7 y = 4 -2x 5x = 7 +8 y = 4 -2x x = 15 : 5 = 3 y = 4 -2*3 = 4 -6 = -2 x = 3 x = 3 y = -2
